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# Quadratic Equations - Word Problems (Grade 10)

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## Quadratic Equations - Word Problems

1.
Determine the price, $p$, that would yield the maximum profit, $P$, for the following profit equation. $P=-170p^2+88000p-55000$
1. $517.65 2.$304.28
3. $258.82 4.$0.63
2.
Suchir throws a ball in the air vertically with a velocity of 40 feet per second. The ball's height above the ground can be modeled by the equation $h(t)=-16t^2+40t+5$ where h is the height in feet and t is time in seconds. When will the ball hit the ground?
1. 2.62 seconds
2. 3.9 seconds
3. 2.02 seconds
4. 3.77 seconds
3.
Given a revenue equation of $R = -250p^2 + 120000p$, find the price where the revenue is at its maximum.
1. $240 2.$480
3. $250 4.$260
4.
Given a profit equation of $P=-100p^2+21850p-800000$, determine the maximum profit, $P$, to the nearest cent.
1. $25.54 2.$30,679.05
3. $50,349.01 4.$393,556.25
5.
A square building with an area of $225 \ m^2$ has a garden surrounding it that has an equal width on all sides. The area of the garden is 1/3 of the area of the building. What is the width of the garden?

6.
The area of the rectangle is 391 square inches. The dimensions of the rectangle are (4x +3) in. and (3x + 2) in. Write an equation and solve for x. Then find the dimensions of the rectangle. 7.
A store rents an average of 725 video games each month at the current rate of $5.50. The owners of the store want to raise the rental rate to increase the revenue to$7000 per month. For each $1 increase in price they rent 25 fewer games each month. A) Write an equation to represent the relationship between the revenue and increase/decrease in the quantity/price of game rentals. B) Can the owners earn$7000/month?

C) What is the best rental price?

8.
Mr. Jones is 5 years older than Ms. Jones, but their actual ages are a mystery. If they tell you that the sum of the squares of their ages is 5,113, how old are they?

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