# 10th Grade Math Solving Equations Word Problems

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# Solving Equations Word Problems

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# Tenth Grade: Solving Equations Word Problems

Simone has 16 player on her soccer team
Simone has 16 player on her soccer team. There are 6 more boys than ...
Sally can paint a house in 4 hours
Sally can paint a house in 4 hours. John can paint the same house in 6 ...
If a ladder is leaning against a building
If a ladder is leaning against a building, and the distance from the bottom of the ladder to the building is 8 ft. less than the length of the ladder, how high up the side of the building is the top of the ladder if the distance is 1 ...
A balloon is rising from the ground
A balloon is rising from the ground at 4 feet per second. Another balloon is at 756 feet and descending at 3 feet per ...
The hypotenuse of a right triangle
The hypotenuse of a right triangle is 16 in. longer than the shortest side and 2 in. longer than the
remaining ...
The area of a triangle
The area of a triangle is 30in2. The base of the triangle measures 2 in. more than twice the height of the ...
The length of a certain rectangle
The length, L, of a certain rectangle is four feet more than three times its width, W. The perimeter of the rectangle is 88 ...
A park is twice as long as it is wide
A park is twice as long as it is wide. It's length is 30...
completing the square
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= -0.002d2 + 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 ...
A ball is shot into the air
A ball is shot into the air. It's height , h in metres after t seconds is modeled by h=-4.9t2 + 30t +1.6...
The sum of the squares of the two
The sum of the squares of the two larger of three consecutive even integers is 12 less than 4 times the square of the smaller ...
A motor boat travels
A motor boat travels 400km. If the boat went 18km/h faster, it could have traveled 600 km in the same amount of ...
Two taps turned on together
Two taps turned on together can fill a tank in 15 mins. Separately, one tap takes 16mins longer than the other tap to fill the ...
Andres and Biloy working together
Andres and Biloy, working together, can build a chicken house in 6 2/3 hours. Andres became ill after 3 hours of working with Biloy, and Biloy finished the job, continuing to work alone in 8 1/4 more ...
A rectangle corral is to be built
A rectangle corral is to be built using 70m of fencing. If the fencing has to enclose all four sides of the ...
Three consecutive even integers
Three consecutive even integers are such that the square of the third is 100 more than the square of the ...
You are selling tickets for a high school basketball game
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...
The perimeter of a rectangular
The perimeter of a rectangular lawn is 24m. If the area of the lawn is 35m2...
The sum of the squares
The sum of the squares of two consecutive positive numbers is 61...
Bob, driving a new Ford
Bob, driving a new Ford, travels 330 miles in the same amount of time it takes John, driving and old Chevy and traveling 10 miles per hour faster, to travel 390 ...
One positive integer is 8 less
One positive integer is 8 less than twice another and the sum of their squares is 244
A model rocket is shot into the air
A model rocket is shot into the air and its path is approximated by h = -5t2 + 30t where h is the height of the rocket above the ground in metres and t is the elapsed time in ...
A software development company is getting ready
A software development company is getting ready to release a new product. The QA Director is notified the following: A Junior Verification Engineer takes 1 hour longer to fix a bug than it takes a Senior Engineer. If they can fix the bug in 5 hours working ...
Suppose that an object is 100 pounds
Suppose that an object is 100 pounds when it is at sea level. Find the value of C that make the equation true. Sea level is 3...
The length of a rectangle is 5 cm less
The length of a rectangle is 5 cm less than twice the width. If the area of the rectangle is 88 cm ...
A rectangular garden is 5 feet longer
A rectangular garden is 5 feet longer than twice its width. It has a sidewalk 3 feet wide on two of its sides. The area of the sidewalk is 213 square ...
You are selling tickets to a high school play
You are selling tickets to a high school play. Student tickets cost \$5 and general admission tickets cost \$8. you sell 566 tickets and collect \$3797...
A framer at a photo gallery
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 ...
How do the Quarter Pounder and Whopper
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 eyes-9 calories in excess of what is allowed on a 1000 calories-a-day ...
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 ...
Suppose you invest \$2000 today
Suppose you invest \$2000 today and you don't add or subtract anything from the money to your investment for 30 yrs. If you earn 12% per year on your investment every year for 30 ...
Frank`s Specialty Coffees makes
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...
There are two phone plans
There are two phone plans. One plan has \$28 one time fee, and 9 cents a min. The second is 13 cents a ...
Shelly can paint a fence in 8 hours
Shelly can paint a fence in 8 hours. Karen can do it in 4 ...
The sum of two numbers
The sum of two numbers is 42. The difference is 14...
9 times the side of one square exceeds
9 times the side of one square exceeds the perimeter of the second square by 1 metre and 6 times the area of the second square exceeds 29 times the area of the first by 1 square ...
Suppose you decide to move your garden
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 ...
Jurassic Park charges \$20 for adults
Jurassic Park charges \$20 for adults and \$12 for children. Total bill for 454 people was \$3860...
Ahmed has first half of a treasure map
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 ...
The perimeter of Mrs. McCord`s rectangular garden
The perimeter of Mrs. McCord's rectangular garden is 100 feet. If the length is 1.5 times longer than the ...
The sum of the squares of two consecutive
The sum of the squares of two consecutive negative even integers is 100...
The height of a batted baseball as a function of time
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(t-2.4)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 ...
A pilot flies 630 miles with a tail wind
A pilot flies 630 miles with a tail wind of 35 miles per hour. Against the wind, he flies only 455 miles in the same amount of ...
completing the square
change to vertex-axis form by completing the square
f(x)=x2+4x-5
The owner of a health foods store
The owner of a health foods store determines that the demand equation for sellin a nutritional supplement is p=18 - 0.5 square root ((x-4) where p is the price of dollars and x is the number of bottles demanded per ...
The sum of two numbers
The sum of two numbers is 26 and their difference is ...
What value of c makes
What value of c makes x2-x+c a perfect square?
A chemical plant is rectangular and has a length
A chemical plant is rectangular and has a length of a hundred meters and a width of sixty meters. A safety zone of uniform width surrounds the plant. if the area of the safety zone equals the area of the ...
The difference of a positive number
The difference of a positive number and its square is -30...
Ruby is 6 years younger than Carlo
Ruby is 6 years younger than Carlo. The average of their ages now, is twice Ruby's age 5 years ...
A company borrowed 600,000 for one year
A company borrowed 600,000 for one year. Part was at 8% interest, part was at 10% interest rate. How much at each rate if annual interest is \$53...
Alvin is 15 years older than Elga
Alvin is 15 years older than Elga. The sum of their ages is 85...
Tickets to a movie cost
Tickets to a movie cost \$7.25 for adults and \$5.50 for students. A group of friends purchased 8 tickets for \$52.75...
A parallelogram has a base
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)
Aprroximately 4.5 million wrecked cars
Aprroximately 4.5 million wrecked cars are recycled in two consecutive years. There were 700,000 more recycled the second year than the first ...
Flex drove 800 miles in x hours
Flex drove 800 miles in x hours on Monday
a) write a rational expression for his average speed.
b) On tuesday he drove for 6 hours at the same average ...
A rectangular patio is 7 ft longer
A rectangular patio is 7 ft longer than it is ...
The total proceeds from a used book sale
The total proceeds from a used book sale were \$115. A total of 65 books were sold. The books were priced at \$1.50 and \$2.00 each. How many books were sold for \$1...
There are a total of 126 cats and dogs
There are a total of 126 cats and dogs at an animal shelter. For every 5 dogs, there are 4 ...
The length of a rectangle is 4 feet longer
The length of a rectangle is 4 feet longer than twice its width. If the area is 96 square ...
A rectangle`s width is 4 times the length
A rectangle's width is 4 times the length. The perimeter is 30 ...
The perimeter of a court is 108 meters
The perimeter of a court is 108 meters.  If the length is 6 meters longers than twice the ...
Rudy must play 12 commercials
Rudy must play 12 commercials during his 1-hr radio show. Each commercial is either 30 sec or 60 sec long. If the total commercial time during that hour is 10 ...
The side of a square house is 24 ft long
The side of a square house is 24 ft long, and the house is located on a lot which is 50 ft longer than it is wide. The perimeter of the lot is 20 ft more than 5 times the perimeter of the ...
Two houses are for sale on the same street
Two houses are for sale on the same street. The second house has 1000 square feet less than twice the square feet of the first house. Together the houseshave 4400 square ...
A 240 inches pipe is cut into two pieces
A 240 inches pipe is cut into two pieces. One piece is 3 times the length of the ...
Two rental airplanes were flown
Two rental airplanes were flown a total of 54 hours in one month. One plane rents for \$105/h, and the other rents for \$130/h. The total income from the two planes was \$6570...
The length of a rectangle is 2 feet more
The length of a rectangle is 2 feet more than twice the width. The perimeter of the rectangle is 40 square feet. Find the length and width of the rectangle. (Hint: First write the length using an algebraic expression that contains width)
Danny had \$22.00 in loonies and toonies
Danny had \$22.00 in loonies and toonies.
a) Write a linear relation for the total amount of money in terms of the number of loonies and toonies.
b) Write an equation to express the number of toonies in terms of the number of ...
A 240-inch pipe is cut into 2 pieces
A 240-inch pipe is cut into 2 pieces. One piece is 3 times the length of the ...
A man buys x cans of beer
A man buys x cans of beer at 30 cents each and (x+4) cans of lager at 35 cents each. The total cost is \$3.35...
Two numbers have a sum
Two numbers have a sum of 127.  The larger is 17 more than the ...
A piggy bank contains 20 coins
A piggy bank contains 20 coins, consisting of nickels and dimes. How many of each type of coin are there if the piggy bank contains \$1...
Rudy must play 12 commercials
Rudy must play 12 commercials during his 1-hr radio show. Each commercial is either 30 sec or 60 sec long. If the total commercial time during that hour is 10 ...
If the length of each side of a square is decreased
If the length of each side of a square is decreased by 4 inches, the perimeter of the new square is 10 inches more than half the perimeter of the original ...
A supplier gives a quote for you
A supplier gives a quote for you: \$3000 for 500 t-shirts; \$5500 for 1000
t-shirts.

Assume there is a linear relationship between the number of t-shirts ordered (n) and the total cost (C)...
Find the area of a circular flower bed
Find the area of a circular flower bed with a diameter of 54 feet.
Car 1 leaves St. Louis at 12 noon
Car 1 leaves St. Louis at 12 noon, traveling at 52mph. Car 2 leaves St. Louis at 2 pm, but travels at 72mph, going in the same ...
At the animal shelter
At the animal shelter there were 46 cats and dogs. There were 18 more dogs than ...
Four times a number
Four times a number is 21 more than the number.
Find an equation of variation y
Find an equation of variation y varies jointly as w and the square of x and inversely as z, y=25 when x=5 w=5 and z=10

I need help with solving equations with variables on both sides.
December 8, 2008, 2:40 pm