Inequalities Word Problems
In mathematics, an inequality is a statement about the relative size or order of two objects, or about whether they are the same or not. The notation a < b means that a is less than b. The notation a > b means that a is greater than b. The notation a ≠ b means that a is not equal to b, but does not say that one is greater than the other or even that they can be compared in size. In each statement above, a is not equal to b. These relations are known as strict inequalities. The notation a < b may also be read as "a is strictly less than b". In contrast to strict inequalities, there are two types of inequality statements that are not strict: The notation a ≤ b means that a is less than or equal to b (or, equivalently, not greater than b) The notation a ≥ b means that a is greater than or equal to b (or, equivalently, not smaller than b)
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The sum of 2 consecutive even integers is at most 400. Find the pair of integers with the greatest sum.

Find all sets of three consecutive positive even integers whose sum is less then 30.

A student scored 71, 83, and 96 on three algebra tests. What must he score on the fourth test in order to have an average grade of at least 85?

The Boston Celtics play an 82game schedule. If they have won 41 of their first 50 games, how many more games must they win at least so that they will have won 70% of all 82 games?

Five times the difference of a number and 14 is at least 160. Find all possible values for the number.

Two trucks start from the same point at the same time and go in opposite directions. One truck travels at 88km/h and the other travels at 72km/h. How long must they travel to be at least 672 km apart?

Assume that the mathematical model C(x) = 16x + 130 represents the cost C, in hundreds of dollars, for a certain manufacturer to produce x items. How many items x can be manufactured while keeping costs between $525,000 and $781,000?

Students in the school band are selling calendars. They earn $.40 on each calendar they sell. Their goal is to earn more than $327. Write and solve an inequality to find the least number of calendars they can sell and still reach their goal.

Jack`s systolic blood pressure is measure to be 100 mm HG. If the measurement error is + 5 mm HG, write an absolute value inequality that represents his probable systolic blood pressure.

The sum of Emma`s age and Julia`s age is sixty. Julia is four times older than Emma. How old is Julia?

Ian wants to promote his band on the internet. Site A offers website hosting for $4.95 per month with a $49.95 startup fee. Site B offers website hosting for $9.95 per month with no startup fee. For how many months would Ian need to keep the website for site B to be less expensive than site A.

Victor`s goal is to earn $75 per week.at his his afterschool job. last month he was within $6.50 of his goal. find the range of amounts that Victor might have earned last month.

There are 5 exams in a marking period. Gerry recieved grades of 70, 78, 90, and 95 on the first 4 exams. What grade must she get on the last exam so that her average for the marking period will be at least 85?

You have saved $52 and deposit $27 every week for 11 weeks. Will you have enough to buy a jacket that cost $340?

A school bus can hold 64 passengers. The 8 White Team has 141 students. How many buses do they need for their field trip?

Elisabeth and Madeline share a cell phone which their parents let them use only between 8pm and 9:30pm. Let x and y represent the number of minutes spent on the cell phone one evening by Elizabeth and Madeline respectively. Write an inequality that models their parents` restriction on the cell phone usage. Skate a graph of the inequality. how would the graph change if the sisters were given special permission to use the phone until 11 pm.

Victor`s goal is to earn $75 per week at his afterschool job. Last month he was within $6.50 of his goal. Find the range of amounts that Victor might have earned last month.

To fit correctly, the width of a machine part can vary no more than 0.01 millimeter from 2.5 millimeters. Write an absolute value inequality to find the acceptable width in millimeters for this machine part?

You need 30 tons of rock to cover the area. If each to costs $60 and each tree is $84, what is the maximum number of trees you can buy with a budget for rock and trees of $2,500. Write an inequality that illustrates the problem and solve. Express the answer as an inequality and explain how you got the answer.

Greg Jones is driving on a straight road that passes through the town of Westview. In Westview, there is a radio station that can be heard anywhere within a 20mile radius of the town. Greg started 50 miles away from Westview at noon, and he is driving at a rate of 40 miles/hour towards it. Write an inequality, valid for the time before Greg reaches Westview, that states that his distance from Westview, expressed as a function of his driving time t (in hours) is less than or equal to 20 miles.


Clark is having a party at his house. His father has allowed him to spend at most $20 on snack food. He`d like to buy chips that cost $4 per bag, and pretzels that cost $2 per bag. Write an inequality to describe the situation.

The post office will charge for the packages, which weigh at least 1 pound and not exceeding 3 pound the same amount.

Animal feed is to be made from corn and soybeans. One pound of corn has 30 units of fat and 20 units of protein, and one pound of soybeans has 20 units of fat and 40 units of protein. What is the minimum toal weight of feed to supply a daily requirement of 2800 units of fat and 2200 units of protein?

Jenny wants to utilize a portion of her garden for growing flowers. Being a designer herself, she visualizes a triangular area with different lengths for each side. For this Jenny decides to keep a side of the triangular area 3 feet shorter and the other 2 feet longer than the third side. She also wants to restrict the perimeter of the triangular area to 32 feet, so that it does not cover a huge area of the garden. Determine the maximum length of each side of the triangular area that Jenny has visualized.

Anne buys a plant whose height is 6 cm. The plant is growing at a rate of 2/3 cm per week. When will its height exceed 10 2/3 cm?

What is the inequality for a graph with points (0,4) and (9,0)


Suppose wheat and sugar are two basic ingredients necessary to bake two items: a loaf of bread and a muffin. A baker has 25 pounds of wheat and 5 pounds of sugar. To bake each loaf of bread, the baker needs to use 1.3 pounds of wheat and 0.5 pound of sugar. To bake each muffin, the baker need needs 0.4 pound of wheat and 0.16 pound of sugar. 1) Set up the inequalities representing the baker’s possible choices for baking the number of loaves of bread and muffins to use up his available resources (wheat and sugar). 2) If each loaf of bread is sold for $2.50, and each muffin is sold for $1.15, define an equation to represent the baker’s revenue function.



Your supervisor allows you to "clockin" for your 8a.m. shift give or take 15 minutes. Let x=8 represent 8 a.m. and x=14.5 represent 2:30p.m.

The absolute deviation of x from 6 is less than or equal to four.



You need 30 tons of rock to cover your backyard area. If each ton cost $60 and each tree is $84, what is the maximum number of trees you can by with a budjet for rock and trees of $2,500?

A manufacturing company has determind that its profits P should be at least 1000000 more then 10 times the number of the manufacturing T. What inequality represent the company`s desired profit?

A person with no more than $25,000 to invest plans to place the money in two investments. One investment is high risk, high yield; the other is low risk, low yield. At least $6000 is to be placed in the highrisk investment. Furthermore, the amount invested at low risk should be at least three times the amount invested at high risk. Find and graph a system of inequalities that describes all possibilities for placing the money in the high and lowrisk investments. Assume x to be high risk, high yield investments and y to be low risk, low yield invesetments.

I want to spend no less than $6000 on a yard project and no more than $10000. Write an inequality representing my budget.



A mixture weighing not more than 78 oz of food A, and food B is to be made so that it contains at last 12 oz of nutrient per unit and the weight of 1 unit is 3 oz. in food B there is 4 oz. If there are x units of food A and y units of food B in the mixture, what is the system of inequalities involving x and y?

Two people plan to share the driving on a road trip. They do not want to drive any more than 9 hours but they want to travel at least 500 miles. One person averages 55 mph and the other averages 70 mph.

The sum of two numbers is less than 15. The second number is 3 more than the first. What are the possible values for the first of the two numbers? In your answer, denote the first number by x.

Abigail drove h hours at rate of 55 mi/h. She did not reach her goal of driving 385 miles for the day. how long did she drive?

You have to be 4ft. tall to ride a roller coaster at the amusment park. Write an inequality for this situation. Let h be height in feet.

Australian football is played on an elliptical field. The official rules state that the field must be between 135 and 185 meters long and between 110 and 155 meters wide. a) Write an equation for the largest allowable playing field. b) Write an equation for the smallest allowable playing field c) Write an inequality that describes the possible areas of an Australian football field

100 fish are caught, tagged and released. Later, 70 fish are caught and 8 of them are tagged. Approximately how many fish are there in the lake?



How do you know if a value is a solution for an inequality?

the opposite of g is at least 5

truck A is rented for $50/day plus $.20 per mile. truck B is rented for $20/day plus $.50 per mile. How many miles must you drive in truck A to make it a better deal than truck B?

In 90% of the last 30 years, the rainfall at Shell Beach has varied no more than 6.5 inches from its mean value of 24 inches. Write and Sold an absolute value inequality to describe the rainfall in the other 10% of the last 30 years.

ruby bought 2 tissues of the same kind and the price. she gave 200and got a change of less than 5. what are the possible price of the blouses?

The sum of two positive integers is 108. One integer is three times as great as the other. Find the integers

Two integers are in the ratio 5:8. If their sum is less than 100, what is that greatest possible value of the smaller integer?

A car rental company has two rental rates. Rate 1 is $35 per day plus $0.16 per mile. Rate 2 is $50 per day plus $0.09 per mile. If you plan to rent for one week, how many miles would you need to drive to pay less by taking Rate 2?

You are waiting in line to buy tickets to see your favorite band. You know you will be waiting at least 80minutes. You are taking some magazines that usually take you 20 minutes a piece to read. How many magazines will you need to bring if you plan to read the entire time you wait?

You have $45.00 to spend at a CD store. The CD`s are $12.99 each. Write an inequality that represents the number, n, of CDs that you can buy without spending more money than you have.

Tickets to the hit musical Peter Pant cost Php 1000 for reserved seat and Php 500 for general admission. If daily receipts must average at least Php 100 000 to meet expenses, graph an inequality that shows the possible ways that the musical can sell reserved tickets (s) and general admission (y).

a hockey team determines that it needs at least 60 points for the season to make the playoffs. a win w is worth 2 points and a tie t is worth 1 point. find and graph an inequality that describes the situation.

for a door to meet specifications at a carpentry shop the width must be within 1/8 inch of the expected width of the door. the shop gets an order for doors that are 3/1/2 feet wide. Which of the following is an inequality that expresses the range of widths for acceptable doors?

Suppose wheat and sugare are two basic ingredients necessry to bake two items: loaf of bread and a muffin. A baker has 25 lbs. of wheat and 5lbs. of sugar. To make each lofa of bread, the baker need to us 1.3 lbs. of wheat and 0.5 lbs. of sugar. To bake each muffin, 0.4 lbs. of wheat and 0.16 lbs. of sugar. Set up the inequalities representing the baker`s possible choices for baking the number of loaves of bread and muffins to use up his available resources (wheat and sugar).

25lbs of wheat and 5lbs. of sugare to make a loaf of bread 1.3 lbs of wheat and 0.5bs of sugar. Set up inequalities to use resource.

Set up inequalities to 25lbs. of wheat and 5lbs. of sugar. To make a loaf of bread use 1.3 lbs of wheat and 0.5 lbs of sugar.

A baker has 25 pounds of wheat and 5 pounds of sugar. To bake each loaf of bread, the baker needs to use 1.3 pounds of wheat and 0.5 pound of sugar. To bake each muffin, the baker needs to use 0.4 pound of wheat and 0.16 pound of sugar. A) Set up the inequalities representing the baker’s possible choices for baking the number of loaves of bread and muffins to use up his available resources (wheat and sugar). B) If each loaf of bread is sold for $2.50, and each muffin is sold for $1.15, define an equation to represent the baker’s revenue function.

You are planning to spend no less than $6000 and no more tahn $10,000 on your landscaping project. Wrire an inequality that demonstaes how much money you will willing to spend on the project.

Zachary can spend no more that $94 per day to rent a car. A car rents for $30 per day plus $0.20 per mile. What is the maximum number of miles that he can drive the car?

Suppose you are setting up a small business and have invested $16,000 to produce an item that will sell for $5.95. If each unit can be produced for $3.45, how many units must you sell to break even?

For $16 yu can purchase a membership card which entitles you to rent movies for $2.75 each instead of $3.50 each. At least how many movies would you have to rent before you save money by purchasing the membership card?

A total of 50 jubiors and seniors were given a mathmatic test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What was the average score for all 50 students who took the test?

a length of 4.2 cm with a tolerance of 0.01 cm


b) Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of trees you can buy with a budget for rock and trees of $2,500? 8 30 tons x $60= $1,800 allowed for rocks Budget=$2,500$1,800 for rocks = $700 allowed for trees 8 x $84= $672 which will keep us under budget and below $700

Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of trees you can buy with a budget for rock and trees of $2,500? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.

A rectangle has a base of x m and a height of ym. If the perimeter of the rectangle is at least 10 m but no more than 20 m indicate the possible paired values (x,y) as a shaded region on a graph.

Most fish can adjust to a change in the water temperature of up to if the change is not sudden. Suppose a lake trout is living comfortably in water that is Write an absolute value inequality that represents the range of temperatures at which the lake trout can survive.

The sides of a triangle are in the ratio of 5:6:7. If the perimeter is no more than 54m, what is the largest number the longest side can be.

Building a ski ramp. Write an inequality in the variable x for the degree measure of the smallest angle of the triangle shown in the figure, given that the degree measure of the smallest angle is at most 30°. The values of the triangle given are x, x+8, and a ?

a motor boat travels 36 km downstream in 2 hours. in coming back upstream, the trip takes 3 hours. find the rate of the boat in still water and the rate of the current.


the grades for a course are based on 5 exams and 1 final. All six of the tests are worth 110 points. In order to receive an A in the course you must earn at least 550 points. Your grades on the 5 exams are as follows: 88, 96, 93, 82, 90. Write an inequality that represents the various grades you can earn on the final and still get an A. Solve the inequality

Jenny wants to utilize a portion of her garden for growing flowers. Being a designer herself, she visualizes a triangular area with different lengths for each side. For this Jenny decides to keep a side of the triangular area 3 feet shorter and the other 2 feet longer than the third side. She also wants to restrict the perimeter of the triangular area to 32 feet, so that it does not cover a huge area of the garden. Determine the maximum length of each side of the triangular area that Jenny has visualized

Shirley buys a plant whose height is 6 cm. The plant is growing at a rate of two thirds cm per week. When will its height exceed 10 and two thirds cm?


1. Jenny wants to utilize a portion of her garden for growing flowers. Being a designer herself, she visualizes a triangular area with different lengths for each side. For this Jenny decides to keep a side of the triangular area 3 feet shorter and the other 2 feet longer than the third side. She also wants to restrict the perimeter of the triangular area to 32 feet, so that it does not cover a huge area of the garden. Determine the maximum length of each side of the triangular area that Jenny has visualized.

rate 1 is $35 per day plus $0.16 per mile. Rate 2 is $50 per day plus $0.09 per mile. If you plan to rent for one week, how many miles would you need to drive to pay less by taking Rate 2?

Mary wants to buy a pair of shoes and a dress. The shoes costs twice as much as the dress. She only has $300 to spend. What is the most she can spend for the shoes?

At what rate will $5000 earn $1200 interest in 3 years?

The specifications for machined parts are given with tolerance limits. For example, if a part is to be 6.8 cm thick, with a tolerance of .01 cm, this means that the actual thickness must be at most .01 cm, greater than or less than 6.8 cm. Between what 2 two thicknesses is the dimension of the part acceptable? Write an absolute value equation using "d" as the variable. Write, as well, the set notation, and interval notation that models this situation.

A baker has 25 pounds of wheat and 5 pounds of sugar. To bake each loaf of bread the baker needs to use 1.3 pounds of wheat and 0.5 pounds of sugar. To bake each muffin the baker will need to use 0.4 pounds of wheat and 0.16 pounds of sugar. 1) Set up the inequalitied representing the bakers possible choices for baking the number of loaves of bread and muffins to use up his available sources (wheat and sugar. 2) If each loaf of bread is sold for $2.50 and each muffin is sold for $1.15, define an equation to represent the bakers revenue function.

90% of the time, rainfall in Seal Beach has not varied more than 6.5" from its mean value of 24". Write an absolute value inequality to describe the rainfall in the other 10%.

Suppose wheat and sugar are two basic ingredients necessary to bake two items: a loaf of bread and a muffin. A baker has 25 pounds of wheat and 5 pounds of sugar. To bake each loaf of bread, the baker needs to use 1.3 pounds of wheat and 0.5 pound of sugar. To bake each muffin, the baker need needs 0.4 pound of wheat and 0.16 pound of sugar. 1. Set up the inequalities representing the baker’s possible choices for baking the number of loaves of bread and muffins to use up his available resources (wheat and sugar). 2. If each loaf of bread is sold for $2.50, and each muffin is sold for $1.15, define an equation to represent the baker’s revenue function.


highest january temp. was 98deg farenheit in 1954. Lowest Jannuary temp. was 80 degree Farenheit. write an inequality that represents the various temps in the united states in January.

The product of 4 and a number is at least 35.

Ronal wants to sell his car through a broker who charges a commission of 10% of the selling price. Ronald still owes $11,025 on the care. Ronald must get enought to at least pay off the loan. What is the range of the selling price?

Jan`s account balance is $3800. Of this, $750 is for rent. Jan wants to keep a balance of at leat $500. Write and solve an inequality describing how much she can withdraw & still meet these conditions

Four times the sum of twice a number and 3 is less than 5.5 times that same number

A cellular phone company offers a contract for which the cost C, in dollars, of t minutes of telephoning is given by C=0.25(t400)+74.95, where it is assumed that t ≥400 minutes. What times will keep cost between $119.20 and $153.70?

a ball is thrown straight upward from the top of a building 128 feet high with an initial velocity of 48 feet/second, has a height, in feet, of h(t) = 16t2 + 48t + 128 t seconds later. for what time interval will be ball be at least 64 feet above ground?

The largest egg laid by any bird is 8 inches long. the smallest egg is 0.4 inch in length. write an inequality that represents the various lengths of bird eggs.

A man has $10.00 to buy stamps. He wants to buy twice as many $0.22 stamps as $0.14 stamps. What is the greatest number of $022 stamps he can buy?

you have $50 and you are going to an amusement park. You spend $25 for the entrance fee and $15 for food. You want to play a game that costs $.75. Writes and solve an inequality to find the possilble numbers of times you can play the game. If you plat the game the maximum number of times, will you have spent the entire $50? Explain.

A salesman`s monthly commission is 15% on all sales over $12,000. If his goal is to make a commission of at least $3000 per month, what minimum monthly sales figures must he attain?

susan has 75 and 78 on her first two tests what grade would she need to make to have atleast an 80? Set up as inequality.

you have 95 votes & your opponent has 120 votes. 45 more students will be voting. let x represent the number of students (out of 45) who vote for you. write inequality that shows the values of x that will allow you to win

mrs. hays has promised her two teenagers tto a concert if together they save more than $25.00 of their spending money. the older teenager agrees to save twice as much as the younger . how much must ech save?

Determine what kind of number can be divisible by 2 0,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30. What do you notice?

shopping for new car. x=price of new car plus 5% sales tax , plus 144.00 for title and liscence. will spend less than 9,970 total. What is the price range?

Mrs. Denney is renting a car that gets 35 miles per gallon. The rental charge is $19.50 a day plus 18 cents per mile. Her company will reimburse her for $33.00. If Mrs. Denney rents the car for 1 day, find the maximum number of miles that will be paid for her company.

55 to 60 tiles are needed to retile a floor. each tile costs $6.25. write and solve a compound inequality to determine what the cost c of the tile could be.

nine less than a number is at most that same number divided by 2

Katie wants to buy the newest barbie doll set she only has $5 saved how much does katie needs to have before she can buy the barbie if it cost $24 ?

If the average temperature in Hawaii is 83 degrees Fahrenheit plus or minus 15 degrees, write an absolute value inequality representing the temperature in Hawaii.

there are 88 keys on a new piano. if there are 12 pianos in a room of broken pianos, some of which may have missing keys, how many piano keys could be on the piano?

The 2 coins in Danielle`s piggy bank have a vlaue of at least $1.44. The bank contains only nickels and dimes. What is the fewest number of dimes that could be in the bank?

The 25 coins in Danielle\`s piggy bank have a vlaue of at least $1.44. The bank contains only nickels and dimes. What is the fewest number of dimes that could be in the bank?


spend no less than 6,000 and no more than 10,000

In a right triangle one of the acute angles x is less than 3 times the other acute angle plus 10 degrees. Solve for x.



jabari is training for a marathon


The lenghts of the legs f an isosceles triangle are integers. The base is half as long as each leg. What are the possible lenghts of the legs if the perimeter is between 6 units and 16 units?

Bob has 11 more than twice as many M&M`s as Tom. Brenda has 15 less than Bob. If they have 107 M&M`s all together, how many does each person have?

Amber is car shopping. She doesn`t want to spend more than $12,000. The state tax is 7% and registration is $190. What is the price range for her car taking into account the tax and registration?

you and some friends go out for pizza. Together tiy have $32. You want to order two large pizzas with cheese at $10 each. Each additional topping cost $0.60 and each small soft drink costs $1.00. Write an inequality that represents the numbers of toppings (x) and drinks (y) that your group cab afford. (Assume there is no sales tax). Sketch a graph of the solution of the inequality.

In a Winter Olympics 5000 meter speedskating events, Hans Holden scored times of 6.85, 7.04, and 6.92 minutes on his first three trials. Use and inequality to find the times he can score on his last trial so that his average time is under 7.0 minutes.


write an inequality to compare the number of endangered birds and clams. the table show there are 62 clams endangered and 14 more birds than clams

Your quiz grades are 73, 75, 89 and 91. What is the lowest grade you can obtain on the last quiz and still achieve an average of at least 85?


twice the sum of a number and 4 is less than 12

what volume in ml of a 60% hydrochloric solution must be addes to 100 ml of 30% hydrochloric solution to make 36% hydrochloric solution


Metro Concerts can rent a truck for either $55 with unlimited mileage or $29 plus 40 cents per mile. For what mileages would the unlimited mileage plan save money? a.Write an inequality to describe the situation. b.Solve the inequality.

Metro Concerts can rent a truck for either $55 with unlimited mileage or $29 plus 40 cents per mile. For what mileages would the unlimited mileage plan save money? a. Write an inequality to describe the situation. b. Solve the inequality.

The heights of the student in the chrous at Central Middle School vary no more than 4.5 inches from the average height of 57.5 inches .Write and solve an absolute inequality to describe the range of heights of these students .


The making of bookmarks and calendars involve two activities, printing and laminating. These items are made using a special paper. One ream of this paper (100 sheets). Each sheet of paper could make either 2 calendars or 4 bookmarks. Each bookmark requires 30 seconds of printing and 1 minute of laminating. Each calendar requires 1 minute of printing and ninety seconds of laminating. Given that the total time available for printing is 2 hours and the time available for laminating is 3 and a 1/2 hours Clearly define variables, show the model that represents the information in this problem

Akram drove from Rochester to Albany, a distance of 219 miles. AFter the first 1.5 hours of travel, it began to snow and he reduced his speed by 26 miles per hour. It took him another 3 hours to complete the trip.


Kori has at most $21 to spend at a convenience store. She buys a bag of potato chips and a soda for $2.35. If gasoline at this store costs $2.70 per gallon, how many gallons can Kori afford to buy for her car, to the nearst tenth og a gallon?

twenty less than a number is more than twice the same number

Shelly is 3 years older than michele. Four years ago the sum of their ages was 67. Find the age of each person now.

The sum of three times a number and 7 more than the number is the same as the difference between 11 and twice the number.What is the number?

the ages in years of 3 brothers are consecutive multiples of 4. three years ago the sum of their ages was less than 39. find their present ages.

Two girls agree to go on a road trip together. They travel (x + 5) miles on the first day. On the second day they travel 2 miles more than half of the distance they travelled on the first day. On the third day they drove 3 times as far as they did on the second day. If they drove 5000 miles total, find the value of x.

Mr.green needs to buy Algebra 1and Alegbra 2 books for the mathematics department. Algebra 1 books cost $85 each and Algebra 2 books cost $94 each. Mr.green has $20,000 to spend and needs to buy 120 Alegbra 2 books.What is the maximum number of Algebra 1 books he can buy ?

Suppose wheat and sugar are two basic ingredients necessary to bake two items: a loaf of bread and a muffin. A baker has 25 pounds of wheat and 5 pounds of sugar. To bake each loaf of bread, the baker needs to use 1.3 pounds of wheat and 0.5 pound of sugar. To bake each muffin, the baker need needs 0.4 pound of wheat and 0.16 pound of sugar. 1) Set up the inequalities representing the baker’s possible choices for baking the number of loaves of bread and muffins to use up his available resources (wheat and sugar). 2) If each loaf of bread is sold for $2.50, and each muffin is sold for $1.15, define an equation to represent the baker’s revenue function. 3) Graph the 2 inequalities in 1 and see if you can determine what the optimal mix is.

Reginald`s cement truck can travel up to 300 miles on one tank of gas. Reginald has driven 246 miles so far today, and now he has to make a delivery to a construction site that is 30 miles away. Write and solve an inequality to determine whether Reginald will be able to get to the construction site and back without having to fill his gas tank.

Aisha plans to take figure skating lessons. she can rent skates for $5 per lesson or buy skates for $75. For what number of lessons is it cheaper to buy rather than rent skates?

Reginald`s cement truck can travel up to 300 miles on a single tank of gas. Reginald has driven 246 miles so far today, and now he has to make a delivery to a construction site that is 30 miles away. Write and solve an inequality to determine whether Reginald will be able to get to the construction site and back without having to fill his gas tank.

approximately 30% of the land on Earth is forested, but this percent is decreasing due to construction. Write and gragh an inequality for this situation.


Machine A can produce 30 steering wheels per hour at a cost of $16 per hour.MAchine B can produce 40 Steering wheels per hour at a cost of $22 per hour.At least 360 steering wheels must be made in each 8 hour shift.What is the least cost involved in making 360 steering wheels, if maintence of the machine limits their use no more than 8 consective hours.

A binary search repeatedly dvides records of a sorted file in half until the corret record is found. For example, to find data in record 6 of an 8record file, the binary search will examine records 18, then it would narrow the search to records 58, then 56, then locate the data in record 6. Write absolutevalue statements for the records searched in the first three search intervals.

Marcel is on the 9 cents a minute phone plan. If he wants a call to cost him less than $2.00, how long can he stay on the phone?

The rockets of a Mars probe require oxygen to lift off from the surface and return to Earth. Suppose the probe can produce 0.78 L of oxygen for every kg of water and 0.32 L of oxygen for every kg of carbon dioxide. At least 56 L of oxygen are needed. Let x represent the kg of water available and y represent the kg of carbon dioxide.


the length of a standard basket ball court can vary from 84 to 94 feet, inclusive. Write an absolute value inequality that describes the possible lengths of a standard basketball court.

park charges 6 dollars or admission and .70 for each ride. if you have 20 dollars, what is the maximum number of rides you van go on?

find the greatest possible of integers such that one integer is twice the other and their sum is less than 30

IT WILL TAKE AT LEAST 360 POINTS FOR KIKO`S TEAM TO WIN THE MATH CONTEST. THE SCORES FOR KIKO`S TEAMMATES WERE 94,82,AND 87,BUT ONE OF KIKO`S TEAMMATES LOST 2 OF THOSE POINTS FOR AN INCOMPLETE ANSWER.HOW MANY PONITS MUST KIKO EARN FOR HER TEAM TO WIN THE CONTEST?

compare number of 70 and half as many as fish

write an inequality and solve the product of a number and negative three is at least four less than the number

Bev was offered plan A: a flat salary of $2200 semimonthly or plan B: $1800 semimonthly plus a 5% commission of her sales. If Bev were confident that she could regularly bring in $9200 per month in sales. How much more can she expect to make with the better plan?

For the hawks 80 basketball games next year you can buy seperate tickets for each game at $9 each or you could buy a season ticket for $580 at most how many games could you attend at the $9 price before spending more than the cost of the season ticket?

bill ate 3 apples.Amy ate 2 times as much apples. how many apples did amy eat

During the summer months Terry makes and sells necklaces on the beach. Last summer he sold necklaces for $10 each. His sales averaged 20 per day. Considering a price increase, he took a small survey and found that for every dollar increase he would lose two sales per day. If the material for each necklaces costs Terry $6, what should the selling price be to maximize profit. Determine the profit.

During the first 20 miles of a 50 mile bike race, Roger`s average speed was 16 miles/hour. What must his average speed be during the remainder of the race if he is to finish the race in less than 2.5 hours?

a club decides to sell tshirts for $12 as a fundraiser. It costs $20 plus 8$ per tshirt to make the tshirt. Write and solve an equation to find how many tshirts the club needs to make and sell in order to profit at least $100.

a club decides to sell tshirts for $12 as a fundraiser. It costs $20 plus $8 per tshirt to make the tshirt. Write and solve an equation to find how many tshirts the club needs to make and sell in order to profit at least $100.

Express the statement in terms of an inequality involving an absolute value. The difference of two temperatures T1 and T2 within a chemical mixture must be between 6 degrees C and 15 degrees C.

1. You are planning to spend no less than $6,000 and no more than $10,000 on your landscaping project. a) Write an inequality that demonstrates how much money you will be willing to spend on the project.

During the first 2 mi of a 50 mi race, Roger`s average speed was 16 mi/h. What must his average speed be during the remainder of the race if he is to finish the race in less than 2.5h.

the average speed, s, was between 100 and 120 mph

You buy a 6 foot cable for $15.50 and a 3 foot table for $10.25. What would you expect to pay for a 4 foot table

all real numbers that are between 4 and 6


The average number of cucumber seeds in a package is 25. The number of seeds in the package can vary by three. Find the range of acceptable numbers of seeds in each package.

no less than 6,000 and no more than 10,000

an airplane leaves los angeles for denver at a speed of 420 mph. thirty minutes later, a plane going from denver to los angeles leaves denver, which is 850 miles from los angeles, at a speed of 500 mph. when they meet, how far are they from denver?

Abdul is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges and allows unlimited mileage. Company B has an initial fee of and charges an additional for every mile driven. For what mileages will Company A charge less than Company B?

A teacher needs 2 weeks to cover each chapter in an algebra course. How many chapters can the teacher cover in 16 weeks?

a number decresed by 6, gives the same result as twice the number increased by five. choose the equaction that could be used to find this number,x.

Samuel begins his kindergarten year able to spell 10 words. He is going to learn to spell 2 new words every day. Write an inequality that can be used to determine how many days, d, it takes Samuel to be able to soell at least 75 words. Use this inequality to determine the minimum number of whole days it will take for him to be able to spell at least 75 words.

A truck cna be rented from basic rental for $50 pe day. In addition, you have to pay $0.20 per mile. Cotinental charges $20 per day in addition to $0.50 per mie o rent out the same truck. How many mile must you drive in a day to make the rental cost for basic rental a better deal than that for Coninental?

A truck can be rented from basic rental for $50 pe day. In addition, you have to pay $0.20 per mile. Cotinental charges $20 per day in addition to $0.50 per mie o rent out the same truck. How many mile must you drive in a day to make the rental cost for basic rental a better deal than that for Coninental?

A truck can be rented from basic rental for $50 pe day. In addition, you have to pay $0.20 per mile. Cotinental charges $20 per day in addition to $0.50 per mie o rent out the same truck. How many mile must you drive in a day to make the rental cost for basic rental a better deal than that for Continental?

values of x is the area of the rectangle greater than the perimeter

Most fish can adjust to a change in the water temperature of up to 15 degrees Fahrenheit if the change is not sudden. suppose a lake trout is living comfortably in water that is 58 degrees fahrenheit. Write an absolute value inequality that represents the range of temperature at which the lake trout can survive.

Travel time to the park is at least 3 hours

the band is making a banner whose lenght is 2 feet more than the width . the total lenght of the trim (perimeter) can be no more than 48ft. what are the dimensions of the banner

A manufacturer produces the following two items: computer desks and bookcases. Each item requires processing in each of two departments. Department A_has_55 hours available and department B has_39 hours available each week for production. To manufacture a computer desk requires 4 hours in department A and 3 hours in department B while a bookcase requires 3 hours in department A and 2 hours in department B. Profits on the items are $72 and $23 respectively. If all the units can be sold, how many of each should be made to maximize profits? Let X be the number of computer desks that are sold and Y be number of bookcases sold. Write down a linear inequality for the hour used in Department A 2. Write down a linear inequality for the hours used in Department B

Seven more than a number is at most 24.

18 is at least the product of 6 and a number.

Why do you change the ineauality sign in absolute value in inequalities?

You are planning to spend at least $6,000 and no more than $10,000 on your landscaping project. Write an inequality that demonstrates how much money you will be willing to spend on the project.

spend no less than $6000 and no more than $10,000

The French club is sponsoring a bake sale. If their goal is to raise at least $320, how many pastries must they sell at $2.50 each in order to meet the goal?

If a discount of 20%off the retail priceof a desk saves Mark $45.00, how much did he pay for the desk?

the sum of half a number and two thirds of thenumber is less than 14

There are 461 students and 20 teachers taking buses on a trip to a museum. Each bus can seat a maximum of 52. What is the least number of buses needed for the trip?

2n over 5 + n over 10 4=6+3n15

Clara had 22 coins, dimes and quarters. Altogether the coins are worth more than $3.40. Atleast how many of the coins are quarters?

Celia`s long distance company charges $5.95 per month plus $0.06 per minute. If Celia has budgeted $30 for long distance, what is the maximum number of minutes she can call long distance per month?

The speed limit on highways in Florida is 70 miles per hour. Write and solve an inequality to find how long will it take you to travel the 105 miles from Orlando to St. Augustine if you travel at or below the speed limit.

the length of each side of a certain triangle is 7 less than twice the length of a side of a certain square. What are the smallest possible dimensions of the triangle if the perimeter of the triangle is at least as great as the perimeter of the square.

y2 is less than5 or y2 is greater than 5

a regulation for riding a certain amusement park ride requires a child be between 30 inches and 50 inches tall. What inequality can be used to determine whether or not a child`s height, h, satisfies the regulation?

Jenny wants to utilize a portion of her garden for growing flowers. Being a designer herself, she visualizes a triangular area with different lengths for each side. For this Jenny decides to keep a side of the triangular area 5 feet shorter than the third side and the other side 4 feet longer than the third side. She also wants to restrict the perimeter of the triangular area to a maximum of 29 feet, so that it does not cover a huge area of the garden. Determine the length of each side of the triangular area that Jenny has visualized.

six years ago, Buford was less than half as old as he is now. Write an inequality and find his current age.

If the first and third of three consecutive odd integers are added, the result is 87 less than five times the second integer. Find the third integer

the number of passengers p on the bus is no more than 45

solve 6 < x/2  4 < 3 . Express the solution set in both set builder and interval notations.


The sales representative informs you that there are two floor plans still available, and that there are a total of 56 houses available. Use x to represent floor plan #1 and y to reprensent floor plan # 2

A swimming pool is 7 feet deep as is being filled at the rate of 2.5 feet per hour. How long can the pool be left unattended without the water overflowing?

Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.


The cost of an ad is $1.25 for every 5 words. If Maria wants to spend no moe than $15 on her ad, what is w the maximum number of words she can use?

two trains starting at the same location, travel in opposite directions> One train travels at 90mph and the other at150mph. After some time the trains are more than 700 miles from each other.

the net is atleast 10 yard away

You are planning to spend no less than $6,000 and no more than $10,000 on your landscaping project.

write an inequalityin the variable x for the degree measure of the smallest angle of the triangle shown in the figure, given that the degree measure of the smallest angle is at most 30.


more than 6000, less than 10000

Of the 50 u.s. states 30 states border a major body of water and 14 states border a foreign country. Seven states border both a major body of water and a foreign country. How many states border on just a major onbody of water and how many border on just a foreign country?

Of the 50 u.s. states 30 states border a major body of water and 14 states border a foreign country. Seven states border both a major body of water and a foreign country. How many states border on just a major on body of water and how many border on just a foreign country?

Sam is 8 years older than Sue. Four years ago, Sam was twice as old as Sue. How Old is Sam?

a nursery has 100 flats available for planting two exotic flowers a and b. The seed for exotic flower a costs $4 and the seed for exotic flower b costs $6 per flat. THe total cost of labor will be $20 per flat for flower a and $10 per flat for flower b. The expected income for flower a is $110 per flat and $150 per flat for flower b. If the owner of the nursery does not wish to spend more thatn $480 for seed and $1,400 for labor, how many flats of each exotic flower should be planted in order to obtain the maximum profit?

The car ride will at least 30 minutes.

the amount invested in lowrisk stocks will be at most 1000 more than the amount invested in mediumrisk stocks

x will be at most 1000 more than y

The width of a rectangle is 33 the perimeter is 776 less than the length.

A subway train makes six stops of equal length during it 21 km run. The train is actually moving for 20 min of the trip. At most how long can the train remain at each station if the average speed for the trip, including stops, is to be at least 26 km/h?

Charles wants to raise money for his class trip. He decides to sale pies and cookies. He will sale the pies for $5 and the cookies for $2. He wants to raise $200.

eddie plans to buy a pair of shoes and a pair of jeans. he etimates the the shoes will cost him twice as much as the pair of pants. if he wants to spend no more than $66. how much can he spend on pants?

the base of a triangle is 10 in.Its height is(x+4) in.Its area is no more than 56 in to the second power.What are the possible integer values of x?


Roschelle owns a car and a moped. she has at most 12 gal of gasoline to be used between the car and moped. the cars tank holds at most 18 gal and the moped`s 3 gal. the mileage for the car is 20 mpg and for the moped is 100 mpg. how many gallons of gasoline should each vehicle use if roschelle wants to travel as far as possible. what is the maximum number of miles?

The sum of two numbers is less than . The second number is more than the first. What are the possible values for the first of the two numbers?


A group of students agreed to rent a house for $1200 per month. They found one more person to share the house with and rent decreased by $60 per person per month. How many students ended up renting the house and how much did each pay per month?


The average time a human being can hold their breath underwater is 1 minute. A hippo can hold its breath underwater for at least 5 times as long as a human. Write an inequality that represents how long a hippo can hold its breath underwater.

you are trying to run 5 miles in less than 30 minutes. you run the first mile in 5 minutes, the second mile in 7 minutes, the third mile in 8 minutes, an the fourth mile in 6 minutes. write solve an inequality that represents the time in which you must run the last mile in order to run 5 miles in less than 30 minutes

the length of a rectangle is 1 cm greater than twice the width. If each dimension were increased by 5 cm, the area would be at least 150 cm greater. Find the least possible dimesions

A certian diet requires at least 60 units of Carbohydrates, 45 units of protein, and 30 units of fat each day. Each ounce of Supplement A provides 5 units of carbohydrates, 3 units of Protein, and 4 units of fat. Each ounce on Supplement B provides 2 units or carbohydrates, 2 units of protein, and 1 unit of fat. If supplement A costs $1.50 an ounce and Supplement B costs $1.00 per ounce, how many ounces of each supplement should be taken daily to minimize the cost of the diet?

A square floor is tiled with black and white square tiles. The tiles on the two diagonals are black. If there are 101 black tiles in the floor, what is the total number of tiles in the floor?

Jumping rope can burn 600 calories per hour. Write and solve an inequality to find the number of hours of jumping rope that it would take for you to burn at least 450 calories.

I will be spending no less than $6,000.00 but no more than $10,000.00

kim works in the shipping department loading shipping crates with boxes. each empty crate weighs 150 lb. how many boxes each weighing 35 lb can kim put in the crate if the total weigh is to be no more than 850 lb?

a wedding coordinator estimates that the Ramirezs` wedding will cost approximately 18000. thw wedding coordinator has to stay within 1500 of the estimated amount. write the absolute value inequality to show the cost boundaries of the Ramirezs` wedding

b) Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of trees you can buy with a budget for rock and trees of $2,500? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer.


The weather forecaster stated that the temperature has changed 20 degrees F over the past 6 hours. If the temperature is now 67 degrees F, write an expression using abolute values showing the possible values of the temperature 6 hours ago. What are those values?

you invested a portion of $32,000 at 9% interest and the balance at 11% interest. How much did she invest at each rate if her total income from both investments was $3,200?

A movie ticket costs $3 for a child and $5 for an adult. $500 money was raised and 350 tickets were sold

b) Suppose you want to cover the backyard with decorative rock and plant some trees as the first phase of the project. You need 30 tons of rock to cover the area. If each ton cost $60 and each tree is $84, what is the maximum number of trees you can buy with a budget for rock and trees of $2,500? Write an inequality that illustrates the problem and solve. Express your answer as an inequality and explain how you arrived at your answer


At Seabreeze Amusement Park, to ride the Vortex, you must be at least 44 inches tall, and if you want to ride the TBirds, the maximum height is 55 inches.Either write or graph the an inequality on a number line that describe how tall you must be to go on both of these rides on the same day.

the average numbers of cucumber in a pakage is 25. The nuber of seens in a the pakage can vary by 3. find the range of acceptable numbers of seeds in each package..

To win a bowling trophy, you need a 3game total score of at least 500. On the first two games, your scores are 183 and 165. What score do you need on Game 3?

The force exerted on a spring is proportional to the distance the spring stretches from its relaxed position. Suppose you stretch a spring distance d in inches by applying force f in pounds. For a certain spring, d/f=0.8. You apply forces between 25 and 40 pounds, inclusive.

You want to spend no less than 6000 and no more than 10000

A botique can sell 50 dresses weekly at $120 each and it can sell 30 dresses weekly at $180 each. Determine the demand law, assuming it to be linear

The formula C = 2x + 16 represents the estimated future cost of yearly attendance at State University, where C is the cost in thousands of dollars x years after 2002. Use a compound inequality to determine when the attendance costs will range from 28 to 36 thousand dollars.

the nathional hurricane cener issues a huricane warning if substained winds of 7 miles per hour or higher associated with a urricane areexpected in a coastal ares. write an inquakity showing the wind speeds for which a hurricane warning is issued.

the nathional hurricane cener issues a huricane warning if substained winds of 74 miles per hour or higher associated with a urricane areexpected in a coastal ares. write an inquakity showing the wind speeds for which a hurricane warning is issued.

The school system is trying to help their students be most successful. They are going to hire tutors to help. They must have more teachers than tutors. The maximum number of teachers and tutors to be hired is 50. How many tutors and how many teachers can they have? a.write an inequality that represents the statement that the number of teachers hired must exceed the number of tutors hired. b.write an inequality that represents the statement that the maximum number of teachers and tutors is 50. c.choose a point that satifies the situatuation, and explain why you chose that numbe of tutuors and teachers.

Tom wants to buy 5 baseballs. He hs $20. What is the most each baseball can cost?

If you had 40 multiple choice questions and `x` represents the number of questions answered correctly, how many questions would you need to answer correctly in order to receive a grade of A (90%  100%)?

If you had 40 multiple choice questions and \`x\` represents the number of questions answered correctly, how many questions would you need to answer correctly in order to receive a grade of A (90%  100%)?


The organizers of a drama club wanted to sell 350 tickets to their show. The actual sales were no more than 35 tickets from this goal. Write and solve an absolute value inequality to find the range of the number of tickets that may have been sold.

on average juan uses 350 of airtime per month.company M offers a cell phone plan of $70 dollars plus $.85 for each minute of airtime.company V offers a cell phone plan of $130 per month plus $.65 for each minute of airtime.juan choses company V.Which inequality would show that this plan is cheaper for him??

The two numbers is 24. The larger of two numbers is four less than twice the smaller. Find the numbers

Mr. Belen is thrice older than his son. How old the fatherand the son if the sum of their age is 40?

A number increased by seven is at least five times a number.

a number increaded by seven is at least five times a number.

Only 5 fish can be caught in a day, how many fish can you catch in a month

Grace has twice as much money as Tad. Together they have $36. How much money does Tad have?

Kate has $4 more than twice as much money as Joe does. Joe has $16 less than Marcia does. In all they have $220. How much money does Joe have?

faustino sold two antiqe desks for $280 and $305 how much should he charge for the third in order to average at least $300 per desk?

miss kuhl has 24 students in her class. she is going to divide them into groups of no more than 4 students. how many groups, g, can the students be divided into?

Ball bearings are produced in a factory. A ball bering is acceptable if its diameter is within 3mm of the target of 50 mm. Let x represent the diameter of a ball bearing. Write an absolute value inequality that represents the range of diameters that are acceptable.


The low temperatures for the previous two days were 62 and 58 . We would like to find all temperatures for the third day such that the average daily temperature is at least 64 .

Twice w is at least two more than w

42% of the population supports mayor , margin of error is < 4%. actual percentage of population is p. find the equation

Phil has a strip of wood trim that is 16 feet long. He needs 5foot pieces to trim some windows. What are the possible numbers of pieces he can cut out?

five times a number decreased by eight is at the most ten more than twice the number

two sides of a triangle have the same length. the third side is 20m longer than ach of the other side.the perimeter is no less than 95m.atleast how long are the sides of each?

The computer club wants to buy pizza and soda for a party. The club can get large pizzas for $10 and cases of soda for $3.50. They have a $90 budget. They would like to buy at least 5 large pizzas and 3 cases of soda.

The sum of two consecutive even integers is greater than 88. Find the pair with the smallest sum.

Stace sells electronic supplies. Each week he earns $190 plus a commission equal to 4% of his sales. This week his goal is to earn no less than $500. Write and solve and inequality to find the amount of sales he must have to reach his goal.

You are planning on spending no less than $6,000 and no more than $10,000 on you landscape project.

A truck can be rented from Basic Rental for $50 per day plus $0.20 per mile. Roadrunners charges $20 per day plus $0.50 per mile to rent the same truck. How many miles must be driven in a day to make the rental cost for Basic Rental a better deal than that for Roadrunners?

Jumping rope can burn 600 calories per hour. Write and solve an inequality to find the number of hours of jumping rope that it would take for you to burn at least 450 calories.