Question

A community theater uses the function \small p\left(d\right)=-4d^2+200d-100 to model the profit (in dollars) expected in a weekend when the tickets to a comedy show are priced at \small d dollars each. Write and solve an equation to find out the prices at which the theater would earn $1,500 in profit from the comedy show each weekend. Explain your reasoning.

Answer 1

Answer:

10 or 40

Step-by-step explanation:

We have the following equation

-4d²+200d-100= 1500

We want all the non zero on one side and so we subtract 1500

-4d²+200d-1600=0

Solve for d

4( -d²+50d-400)=0

factor (I can explain this part in depth if needed)

4(d-40)(d-10)=0

d=40

d=10

This means that the price either needs to be 40 or 10 dollars