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Quadratic Equations - Word Problems (Grade 10)

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Quadratic Equations - Word Problems

1. 
Determine the price, [math]p[/math], that would yield the maximum profit, [math]P[/math], for the following profit equation. [math]P=-170p^2+88000p-55000[/math]
  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 [math]h(t)=-16t^2+40t+5[/math] 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 [math]R = -250p^2 + 120000p[/math], find the price where the revenue is at its maximum.
  1. $240
  2. $480
  3. $250
  4. $260
4. 
Given a profit equation of [math]P=-100p^2+21850p-800000[/math], determine the maximum profit, [math]P[/math], 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 [math]225 \ m^2[/math] 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.
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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