Question

Below are the supply and demand equations for stereo headphones in a certain market. In these equations, p represents price, D represents demand, and S represents supply.
D = StartFraction negative 5 over 9 EndFraction p + 94
S = 3 p minus 160
What is D at the point of equilibrium, to the nearest whole number?
a.
151
b.
104
c.
71
d.
54

Answer 1

Set D = S: (-5/9)p + 94 = 3p - 160.
Solve: multiply by 9 → -5p + 846 = 27p - 1440 → 32p = 2286 → p = 71.4375.
Then D = (-5/9)(71.4375) + 94 = 54.3125 ≈ 54.

Answer: d. 54