Absolute Value Word Problems
The absolute value of a real number is its numerical value without regard to its sign. So, for example, 3 is the absolute value of both 3 and −3. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts. Absolute value of a number is the distance from the number on the number line to zero Example: 7 = 7  7  = 7

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.
absolute value word problems

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?
absolute value inequalities word problems

Find the solutions to: 2 x4 + 7 = 3
absolute value inequality word problems

Find the solutions to: 2 x+4 = 6
absolute value equation word problems

Find the solutions to: x+2 = 5
absolute value word problem examples

Which way does the graph of y= 2 x6 +9 open?
absolute value word problems and answers

Which way does the absolute value graph open for y = 3 x+8 +12
absolute value word problem

Which graph is steeper? y = (1/2) x or y = (1/4) x
word problems using absolute value

Where is the vertex of y = (1/2) x3 + 6
Absolute Value Word Problems Worksheet

Where is the vertex of y = 2  x + (1/2)   4
absolute value function word problems

Where is the vertex of the equation y = 3 x+4  6
solving absolute value word problems

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

Find the vertex point of y=2x+5
absolute value equations word problems

In my wallet, I have onedollar, fivedollar, and tendollar bills. The total amount in my wallet is $43. I have four times as many onedollar bills as tendollar bills. All together, there are 13 bills in my wallet. How many of each bill do i have?
absolute value story problems

absolute value word problems examples

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.
absolute value function word problem

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

Julio works as a quality control expert in a beverage factory. The assembly line that he monitors produces about 20,000 bottles in a 24hour period. Julio samples about 120 bottles an hour and rejects the line if he finds more than 1/50 of the sample to be defective. About how many defective bottles should Julio allow before rejecting the entire line?
absolute value inequality word problems worksheet

Phil told his friend that if you subtract 12 from his age and then take the absolute value, you`ll get an average of 3. How old is Phil?
mathematicians use of absolute value function story problems

The average number of cucumber seeds in a package is 25. The number of seeds in the package can vary by 3. Find the acceptable numbers of seeds in each package.
word problem for absolute value

When Annie counted the nickles and dimes she earned at the bake sale there were 325 coins. If the total was $23.15, how many of each kind of coin did she have?
word problems with absolute value

Victor had sold 8 pumpkins for $2.75 each, 9 for $2.00 each, 24 for $1.50 each, and 15 for $10.00 each. He receives 35 cents for each pumpkin sold, plus a $10.00 bonus if he sales $75.00 or more. How much did he earn?
word problems for absolute value equations

The difference between 1 and 7
absolute value inequality word problem

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?
inequality absolute value word problems

Toms ideal weight is 168 pounds. He wants to keep his weight within 3 pounds of his ideal weight. Write an absolute value inequality to describe the acceptable weight.
absolute value equations with word problems

3. In my wallet, I have onedollar, fivedollar, and tendollar bills. The total amount in my wallet is $43. I have four times as many onedollar bills as tendollar bills. All together, there are 13 bills in my wallet. How many of each bill do i have?
absolute value function problems

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.
solving absolute value inequalities word problems

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?
absolute value word problems with answers

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?
solving absolute value equations word problems

ther are 100 kids in a room 10 are tall 20 aare short wat is the value on the kids not tall or short
how to solve absolute value word problems

word problem using absolute value

a length of 4.2 cm with a tolerance of 0.01 cm
glencoe absolute value function word problems

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.
absolute deviation inequalities word problems

a 50gallon fish tank is emptied at a rate of 10 gallons per hour and then filled back up at the same rate until it is full.
temperature problem absolute inequalities

word problems for absolute value inequalities

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
Absolute Value Equations word problem



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.

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%.


I want to know how to solve ratio problems


Sasha’s grade in her math course is calculated by the average of four tests. To receive an A for this course, she needs an average at least 89.5. If her current test scores are 84, 92, and 94, what range of scores can she make on the last test to receive an A for the course?

crissy bought a pack of gum with 24 pieces .the pack of gum had the following flavors : 12.5% watermelon, 0.25 wildberry,and 5/24 grape.


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?




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.


an airplane pilot changed his altitude by 100 meters. describe what this could mean.

Sarah and Jessica are sisters. Sarah`s height is s inches and Jessica`s height is j inches. Their father wants to know how many inches separate the two. Write an equation for this difference in such a way that the result will always be positive no matter which sister is taller.

The test score range in your class frpm 60 to 100. Write an absolute inequality describing the range of the test scores.


Last night`s temperature (t) was at least 10 degrees from freezing (32 degrees Farenheit).

A cereal bar is listed as containing 200 calories. A laboratory tested a sample of the bars and found that the actual calorie content varied by as much as 28 calories. Write and solve an absolute value inequality for the calorie content of the bars.

Sarah and Jessica are sisters. Sarah`s height is s inches and Jessica`s height is j inches. Their father wants to know how many inches separate the two.

In 2005, 24.5% of all Americans were under 18 years old. Rhonda conducts a survey of the ages of students in eleventh grade at her school. On November 1, she finds the average age is 200 months. She also finds that twothirds of the students are within 6 months of the average age. Write and solve an equation to determine the age limits for this group of students. How many months will it be til the first of these students turn 18?

there are ten billion dollars in a safe. A robber comes in and guesses their combination in one try. The combonation was 9/10/04, the birthday of their dog, scruffy. He takes two dollars from the safe. He puts in his solid gold watch and his deed to his house. What happened to the 9 billion and 9 million and 9 hundred and 98 dollars tha were left? what is the absolute value of the safe. How far is the robbery from zero? where does the robber live? Where does he hide the lute? whose safe was it? The robbers name was Panda.

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.


Forensic scientists use the equation h = 2.6f + 47.2 to estimate the height, h, of a woman given the length in centimeters, f, of her femur bone. Suppose the equation has a margin of error of + 4 centimeters and the length of a female skeleton`s femur is 48 centimeters. Write and solve an absolute value inequality that describes the woman`s height in centimeters.


If 7 is added to twice a number and the sum is multiplied by 4, the result is the same 3 times the number minus 2. What is the number

what is the absolute value function shifted nine units to the left?

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.

f(x) = 2 ; x<.2 f(x) = x + 3 ; x>.2

if the runners of the second and third legs run their laps in 53seconds plus or minus 1 second, write an equation to find the fastest and slowest times

all real numbers that are exactly a distance of 4 units away from 2

Barry;s walkie talkie has a range of 2 mi. Barry is traveling on a straight highway and is at mile marker 207. Write and solve an absolutevalue equation to find the minimum and maximum mile marker that Barry`s walkie talkie will reach.

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.

physicians consider an adult`s body temperature to be a normal of it is 98.6 degrees, plus or minus 1 degree. Write anabsolute value inequality that describes this normal temperature range

Leticia sets the thermostat in her apartment to 68 degrees. The actual temperature in her apartment can ar from this by 3.5 degrees. Write an absolute value equation that you can use to find the minimum and maximum temperature.

the average of cindys three test scores must be greater than 70 for her to pass the class. She got a 76 on the last test. she got the same scores on the her first and second test. she passed the class. what scores could she have gotten on the first two tests?

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?

one more than the difference between 18 and seven times a number is negative 9


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?

paris has 24 m&m`s she gave away some to her friends and had 10 left. how many did she give away 24m=10

donna`s new car gets 22 mpg in the city and 34 mpg on the highway. Write a compound inequality which represents the number of miles she can drive on 14 galons of gas. solve.



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.

jack is twice as old as lacy. in 3 years the sum of their ages will be 54. How old are they now?


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

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

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

The mean distance of the earth from the sun is 93 million miles the distance varies by 1.6 million miles find the range of distances of the earth from the sun?

a manufacturer is cutting plastic sheets to make rectangles that are 11.125 in. by 7.625 in. Each rectangle`s length and width must be within 0.005 in. of the desired size. Write and solve inequalities to find the acceptable range length l and width w.

a manufacturer is cutting plastic sheets to make rectangles that are 11.125 in. by 7.625 in. Each rectangle\`s length and width must be within 0.005 in. of the desired size. Write and solve inequalities to find the acceptable range length l and width w.

a quality control inspector at a bolt factory examines randon bolts that come off the assembly line. Any bolt whose diameter differs by more than 0.04 mm from 6.5 mm is sent back. write and solve an absolute value equation to find the maximum and minimum diameters of an acceptable bolt

Ainsley`s school honors outstanding mathematics students at the end of their high school careers with the Mathematics Excellence Award. To earn this award, a student must achieve at least a 90% average in the mathematics sequence, which includes Geometry, Algebra II, Trigonometry, Precalculus, and Calculus. Trigonometry, which is a halfyear course taken concurrently with the second half of Algebra II or the first half of Precalculus (or during the summer), counts for 10% of the award. The other courses are weighted, starting with 15% for Geometry, with a 5 percentage point increase in weight for each fullyear course. Ainsley has earned 80%, 98%, and 85%, respectively, in the first three courses in the sequence. What is the maximum difference in scores she can earn in the remaining two courses and still receive the Mathematics Excellence Award? Extra: Ainsley`s experienced friends say that Precalculus averages five hours of homework per week while Calculus averages eight hours a week. How might this affect Ainsley`s plan? What advice would you offer?


Detective Luis E. Knew that the suspect had traveled from Washington DC to some point 50 miles south on, I 95 and back. He started at 4AM. Luis knows that the suspect has traveled within speed limit (min 40 mi/hr, max 65 mi/hr) in order not to be detected. Find the interval of time within which the suspect must have been outside Washington DC.

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.

Collette is a contestant on a game show. She can win a car if she can guess the price of the car with $725. The price of the car is $16,785. Write and solve an absolute value equation to find the minmum price that collette can guess to win the car

When a number is subtracted from 7, the absolute value of the difference is more than 3. Use interval notation to express the set of all numbers that satisfy this condition.

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 solve an absolute value inequality to describe the rainfall in the other 10% of the last 30 years.

A truck traveling 45 mph and a train traveling 60 mph cover the same distance. The truck travels 2 hours longer than the train. How many hours did each travel?

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?


you have 5 pumpkins. weigh them 2 at atime and you get the following weights in pounds. 110, 112, 113, 114, 115, 116, 117, 118, 120, and 121. how much does each pumpkin weigh?

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?

a meteorologist reported that the previous day`s temperature varied 14 degrees from the normal temperature of 24 degrees. a.what were the minimum and maximum temperatures possible on the previous day? b.Write an absolute value equation for the temperature.

mr. wilson has $2,500 in his saving account and m dollars in his checking account. write an expression that describes the total amount that he has in both accounts.

A car and a bus set out at 2 p.m. from the same point, headed in the same direction. The average speed of the car is 30 mph slower than twice the speed of the bus. In two hours, the car is 20 miles ahead of the bus. Find the rate of the car.

Most meat thermometers are accurate to within plus or minus 2 degrees F. if a meat thermometer reads 160 degrees F, write an equation to determine the least and the greatest possible temperatures of the meat.

the density of a plastic block is listed as 1.7 g/cm3. the manufacturer states that the actual density of the block may vary by as much as 0.03g/cm3. write and solve an absolute value inequality for the range of possible densities of the bloc.

what is three apples plus two yellow apples?


Xavier owns a music store that sells CDs. CD sales this month were 20 more then three times sales for last month. Next month he hopes to double sales for mthis month

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?


all real numbers less than 2 units from 0

the ideal weight of an exercise ball is 175 ounces. Each ball can have an error of 0.35 ounces. What is the range of acceptable weight?

how mayb dogs do you have in one house?



how tall is a tree that is ten feet shorter than a pole that is ten feet its size?

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?

The sum of two consecutive even integers is at most 400. Find the pair of integers with the greatest sum.

Perform each transformation on f(x)=IxI write transformed funcion,g(x) up 3 units

Find the variation constant and an equation of variation where y veries directly as y and x=60 whenx=6

InGeorgia there is a daily limit of 5 largemouth bass that may be caguht.A fIshing license is required with the exception of speCified special dates and places.Annual fishing licenses Cost $9.00 and daily licenses cost $3.50.

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..

If manufactured correctly, a basketball should bounce form 46in to 56 in when dropped from a height of 6ft. determine the tolerance for the bounce height of a basketball and write an absolute value inequality for acceptable bounce heights.


There are 20 people running a 5kilometer race. You have five oranges to give to the runners after the race. If the oranges are evenly divided among the runners, how much of an orange should each runnewr get?


find the critical point of the function f(x)=abs(x+3)1

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.

Jamie has to get an average of 90 on her two tests to pass the level and go on to the next level.On her first test,she got a 92.What are the possiblity test scores that she can get to pass the level?

x is more than 3 units from 9

the absolute value of x9/x5 is greater than or equal to 5

If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? A. 2 hours and 24 minutes


the mean distane of the earth from the sun is 93 million miles. the distance varies by 1.6 million miles. find the range of distances of the earth from the sun.

a box of wheatos breakfast cereal says that it contains 24 onces. How ever, beacause the machinery that fills the boxes cannot be exactally exact

a box of wheatos breakfast cereal says that it contains 24 onces. How ever, beacause the machinery that fills the boxes cannot be exactally exact they can be from 1/8 ounces below to 1 ounce above this weight. write an absolute value inequality for the recommended amount os sleep.

a 747 jumbo jet is approximately the size of a large car in a perfect world puts out 50000 pounds of thrust. however depending on the type of uel and outside air temp the amount of thrust varies by 1600 pounds.

a football team gained 15 yards on the first play and lost 8 yards on the second.

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.

According to a height and weight chart, Mark`s ideal wrestling weight is 186 pounds. Mark will be satisfied if he is no more than 3 pounds from his ideal weight.

ulio works as a quality control expert in a beverage factory. The assembly line that he monitors produces about 20,000 bottles in a 24hour period. Julio samples about 120 bottles an hour and rejects the line if he finds more than 1/50 of the sample to be ...

allyson ans adrian have decided to connect their ankles with a bungee cord; one end is tied to each person`s ankle. The cord is 30 feet long, but can stretch up to 90 feet. They both start from the same location. Allyson moves 10ft/sec and Adrian moves 8ft/sec. Where are the two girls located after 2 seconds?


solve 5^3x1=500 for x to threesignificant digits

does the equation have a slope?does it have a y intercept ?is it in the form of y = mx + b?

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

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 two thicknesses is the dimension of the part acceptable? Show your work.