Question

A graph has quantity on the x-axis and price (dollars) on the y-axis. A demand line goes through (10, 65) and (26, 40). A supply line goes through (0, 20) and (26, 40).
The figure above shows a store’s supply-demand graph for lawn chairs. If the store makes $800 by selling lawn chairs, which of the following is a possible valid price for them?
a.
$50
b.
$40
c.
$25
d.
$20

Answer 1

First get the demand equation. The demand line through (10,65) and (26,40) has slope m = (40−65)/(26−10) = −25/16, so
p = 65 − (25/16)(q − 10) = 645/8 − 1250/p (after substituting q = 800/p).

Substitute q = 800/p (since revenue p·q = 800) and clear denominators:
8p^2 − 645p + 10000 = 0.
Solving gives p ≈ 59.69 or p ≈ 20.94.

From the choices, the closest possible price is $20. Answer: d. $20.