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Tenth Grade: Solving Equations Word Problems
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 ...
The area of a triangle
The area of a triangle is 30in
2. The base of the triangle measures 2 in. more than twice the height of the ...
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= -0.002d
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 ...
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=-4.9t
2 + 30t +1.6...
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 ...
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 ...
A model rocket is shot into the air
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 ...
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 ...
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 ...
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
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 ...
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 ...
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 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 ...
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 ...
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 ...
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)
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 ...
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...
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 ...
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 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...
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 ...
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)...
At the animal shelter
At the animal shelter there were 46 cats and dogs. There were 18 more dogs than ...
