Question

1. A toy company finds there is a linear relationship between p, the price they charge for a playground ball, and n(p), the number of balls they sell during a year. When they charge $3, they sell 8000 balls during the year. However, sales drop to 5200 balls when they charge $5 each.

a. Write an equation for the linear function n(p).
b. Use your function to determine the number of balls they can expect to sell during the year if they charge $6.50 for a ball.

Answer 1

Below in bold.

Explanation:

The general form of a linear function can be written as:

n(p) = kp + C where k and C are constants.

So substituting the given data:

8000 = 3k + C

5200 = 5k + C Subtract

2800 = -2k

k = -1400

and C = 8000 - 3(-1400) = 12200

a. So the equations is:

n(p) = -1400p + 12200

b.

For a charge p of $6.50;

n(p) = -1400*6.5 + 12200

= 3100 balls.