Solving Quadratic Equations Word Problems

The sum of two numbers is 42. The difference is 14. Find the two numbers.
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How do the Quarter Pounder and Whopper with cheese measure up in the calorie department? Actually, not too well. Two Quarter Pounders and three whoppers with cheese provide 2607 calories. Even with one of each provides enough calories to bring tears to Jenny Crag`s eyes9 calories in excess of what is allowed on a 1000 caloriesaday diet. Find the calories in each item.
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A framer at a photo gallery wants to frame a print with a matte of uniform width all around the print. To make it pleasing to the eye, the area of the matte should equal the area of the print. If the print measures 40 cm by 60 cm, how wide should the matte be?
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The sum of two numbers is 26 and their difference is four. Find the numbers.
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A balloon is rising from the ground at 4 feet per second. Another balloon is at 756 feet and descending at 3 feet per second. In how many seconds will the be at the same altitude?
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The path of the ball for many golf shots can be modeled by a quadratic function. The path of a golf ball hit at an angle of about 10 degrees to the horizontal can be modeled by the function, h= 0.002d^{2} + 0.4d, where h is the height of the ball, in meters, and d is the horizontal distance the ball travels, in meters, until it first hits the ground. a) What is the maximum height reached by the ball? b) What is the horizontal distance of the ball from the golfer when the ball reaches its maximum height? c) What distance does the ball travel horizontally until it first hits the ground?
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You have made a quilt that is 4 feet by 5 feet. You want to use the remaining 10 square feet as a decorative border of uniform width. What should the width of the border be?
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In the quadratic formula, if b^{2}  4ac is less than 0, what can you say about the solution?
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In the quadratic formula, if b^{2}  4ac is greater than 0, what can you say about the solution?
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What is b^{2}  4ac called in the quadratic formula?
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quadratic equations word problems

The perimeter of Mrs. McCord`s rectangular garden is 100 feet. If the length is 1.5 times longer than the width, what are the dimensions of the garden?
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change to vertexaxis form by completing the square f(x)=x^{2}+4x5
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One positive integer is 8 less than twice another and the sum of their squares is 244
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Suppose you decide to move your garden away from the house, so you have to use 50 feet of fencing for four sides. The length of the garden must be twice as long as the width. If the area is now 139 feet square, what dimensions should the garden have?
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Frank`s Specialty Coffees makes a house blend from two types of coffee beans, one selling for $9.05 per pound, and the other selling for $6.25 per pound. His house blend sells for $7.37 per pound. If he is using 9lb of the 6.25/lb beans, how many pounds of the $9.05/lb beans does he need to make his house blend?
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Ahmed has first half of a treasure map, which indicates that the treasure is buried in the desert (2x + 6) paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must go to the Castle Rock, walk ‘x’ paces to the North, and then walk (2x + 4) paces to the East. If they share their information, then they can find ‘x’ and save a lot of digging. What is ‘x’?
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You are selling tickets for a high school basketball game. Student tickets cost $3 and general admission tickets cost $5. You sell 350 tickets and collect $1450. How many of each type of ticket did you sell?
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The length of a rectangle is 4 feet longer than twice its width. If the area is 96 square feet, find its width and length.
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A rectangle corral is to be built using 70m of fencing. If the fencing has to enclose all four sides of the corral, what is the maximum possible area of the corral in square metres?
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A parallelogram has a base of length 2x +1 and a height of x+3 and has an area of 42 square units. Find the base and height of the parallelogram. (A=BH)
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A motor boat travels 400km. If the boat went 18km/h faster, it could have traveled 600 km in the same amount of time. What was the original speed of the boat?
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A ball is shot into the air. It`s height , h in metres after t seconds is modeled by h=4.9t^{2} + 30t +1.6. How long to 2 decimal places will it take the ball to reach a height of 35m?
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The height, H metres, of a batted baseball as a function of time, t seconds, since the ball was hit can be modeled by the relation H=2.1(t2.4)^{2}+13. a) what was the maximum height of the ball? b) at what time after it was first hit did the ball reach its maximum height? c) how far off the ground was the ball first hit? d) how long did it take the ball to first hit the ground?
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What value of c makes x^{2}x+c a perfect square?
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The difference of a positive number and its square is 30. Find the number.
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A model rocket is shot into the air and its path is approximated by h = 5t^{2} + 30t where h is the height of the rocket above the ground in metres and t is the elapsed time in seconds. When will the rocket hit the ground?
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An airplane makes a 900km flight with a tailwind and returns, flying into the same wind. The total flying time is 3 hrs 20 mins. The planes speed in still air is 600km/h. What is the wind speed. Answer is 60km/h. How?
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i want to change the carpet in an office that measure 12 feet by 15 feet, if the carpet cost $12.50 per square yard how much is it ?
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Problems on Quadratic Equations

There are 3 times as many houses available with floor plan 2 than there are with floor plan 1. There are 56 houses in total that are available. How many of each floor plan is there?
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You are making a frame of uniform width for a picture that is to be displayed at the local museum. The picture is 3.25 feet tall and 3 feet wide. The museum has allocated 15 square feet of wall space to display the picture. What should the width of the frame be in order tousle all of the allocated space?
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two numbers have a sum of 20. the second is 2 mores than three times the first. find the numbers
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area of a painting a rectangular painting with a width of x centimeters has an area of x^2 + 50x square centimeters. Find a binomial that represents the length.
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suppose that an open box is to be made from a square sheet of cardboard by cutting out 4inch squares from each corner and then folding along the bottom of the cut. If the box is a have a volume of 100 cubic inches find the original dimensions of the sheet of cardboard.
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A number of students rented a car for $160 for a one weekend trip. if another sudent had joined the original group, each person`s share of expenses would have been reduced by $8. How many students were n he original group?

the dolphin jumps out the water at a show, the function can be modeled by f(x)=16x^2X32x, which the x is the time in second. find out what is the max. height, and how long does it take to reach that height, and how long will the dolphine stay in the air before he went back into the water.

A baseball is hit from a height of 1m. It`s height in metres, h, after t seconds is h=4.9t squared +10 +1. What is the maximum height of the ball?

Malcolm is twice as old as sundeep. the sum of their afes is 39

the difference of two integers is 4 and the sum of their reciprocals 4/15. Find the two integers.

in the us house of representatives there are 435 members. if an appropriations bill passes the house with 85 more members voting in favor than against . how many voter in favor and how many voter against

each pail of plaster covers 81 square feet of ceiling. How many pails are needed to cover the ceiling of a square room with walls 25 feet long?

a rectangular lawn measures 7m by 5m. A uniform border of flowers is to be planted along to adjacent sides of the lawn, as shown in the diagram. If the flowers that have been purchased will cover an area of 6.25 m squared, how wide is the border?

family received 19 pieces of mail, consisting of magazines, bills, letters, and ads. If the received the same number of magazines as letters, three more bills than letters, and five more ads than bills, how many magazines did they receive?

# An object is launched at 19.6 meters per second (m/s) from a 58.8meter tall platform. The equation for the object`s height s at time t seconds after launch is s(t) = –4.9t2 + 19.6t + 58.8, where s is in meters. When does the object strike the ground?

A balloon is rising from the ground (#457) A balloon is rising from the ground at 4 feet per second. Another balloon is at 756 feet and descending at 3 feet per ...

One canned drink is 15% orange juice; another is 5% orange juice. How many liters of each should be mixed together in order to get 10L that is 11% orange juice?

Ahmed has the first half of a treasure map, which inducastes that the treasure is buried in the desert (2x+4) paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must go to Castle Rock, walk `x` paces to the North, and then walk (2x+4) paces to the East. If they share their information, then they can find `x` and save a lot of digging. What is `x`?

a tugboat can travel 8 mph in still water.going against a current it spends 1 hour and 20 minutes more than going the same distance of 8 miles with the current.find the rate of the current.



if a number is added to its square the result is 42. find the number?

If the same length is cut off at three pieces of wood measuring 21cm, 42cm and 45cm, the three pieces of wood (not the cut offs) can be assembled into a right triangle. Determine the length that should be cut off each piece.

A rectangle is 4/3 as long as it is wide. A second rectangle is 4 meters longer and 2 meters wider than the first, and its area is twice that of the first. Find the dimensions of the rectangles.

To raise $1,000, the members of the Nice People Club pledged to chip in equal amounts. However, five of the Nice People did not contribute, so to make the $1,000 the rest of the members had to pay a extra $10 each. How much did each paying member contribute?

Five times the square of a number is 980. Find the Number.

find the minimum product of two numbers whose difference is 9

The sum of two positive integers is 80. Find the integers if one number is 8 greater than the other.

1. Bob and Sara went to a restaurant last Saturday. Sara remembers that she had a steak and Bob remembers that he had a burger. Their total bill was $22 but they don’t remember what the cost for each was. Sara remembers that her meal was twice as much as Bob’s. How much was each of their meals?


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A social club charters a bus to go to Six Flags at a cost of $900. At the last minute, 5people decide not to go. This raises the cost per person by $2 each. If the cost is split evenly between all the people who go, how many people originally intended to take the trip? How many did take the trip?

A cannon was shot off a 100ft building to hit a target at 100 feet away. it is launched with an initial velocity of 20ft/second. it took the cannon 3 minutes to reach the target. what was the height of the cannon when it hit the target?

So Wing has made a quilt that is 4 feet by 5 feet. So wants to use the remaining 10 square feet of fabric to add a decorative border of uniform width. What should the width of the boarder be?

suppose you throw a ball over a 10foot fence. barely clearing the fence, the ball reaches its highest point directly above the fence and lands 10 feet from the fence.using the fence as axis of symmetry, write a quadratice equation that models the balls height.

a)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 represent floor plan #2. Write an equation that illustrates the situation. b)The sales representative later indicates that there are 3 times as many homes available with the second floor plan than the first. Write an equation that illustrates this situation. Use the same variables you used in part a. c)Use the equations from part a and b of this exercise as a system of equations. Use substitution to determine how many of each type of floor plan is available. Describe the steps you used to solve the problem. d)What are the intercepts of the equation from part a of this problem? What are the intercepts from part b of this problem? Where would the lines intersect if you solved the system by graphing?

• Determine whether an outfitter leading a backpacking trip would find it more cost effective to make a onetime bulk foods purchase at a buyer’s club with membership fees or purchase the same goods at a conventional supermarket. i need to create variables and arrange an equation from this problem... PLEASE HELP!!!!


a farmer wants to fence 600m. Tell the dimensions

a square is turned into a rectangle by increasing one dimension by 9 and decreasing the other by 3. The area of the rectangle is 5 more than the area of the square. What was the original side of the square?

I need help with an example of a Quadratic word equation using a ball thrown off a roof.


the landing for the steps leading up to a county courthouse is shaped like a trapezoid. the area of the landing is 1500 square feet. the shorter base of the trapezoid is 15 feet longer than the height. the longer base is 5 feet longer than 3 times the height. what is the length of the longer base?

A rectangle has a perimeter of 30 inches. The length is twice as long as the width. What equation could be used to find the length?

A baseball player hits a baseball at a height of 3 feet. A snapshot of the ball shows that as it crossed over second base it had reached a height of 22 feet. It was caught by the center fielder 380 feet away from home plate at a height of 6 feet. A baseball "diamond" is a square with sides of 90 feet.

A farmer grows only sunflowers and flax on his 240 acre farm. This year he wants to plant 80 more acres of sunflowers than flax. How many acres of each crop does the farmer need to plant?

A piece of cardboard is twice as long as it iss wide. It is to be made into a box with an open top by cutting 2inch squares from each corner and folding up the sides. Determine a function V that represents the volume of the box. Find the dimensions.

Ball drops from 70 meter bridge. What is height of ball to the nearest tenth of a meter exactly 2 seconds after ball is released? how many seconds after ball is released will it hit the ground>?

Ball drops from 70 meter bridge. What is height of ball to the nearest tenth of a meter exactly 2 seconds after ball is released? how many seconds after ball is released will it hit the ground?

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