A school uses the function p(t)=t2−20t+175 to model the profit (in dollars) expected in a weekend when the tickets are sold at a certain price, t, to the school musical go on sale a. Write an equation to find out the prices at which the school would earn $100 in profit from the school musical each weekend. b. Find out at what prices the tickets should be sold at to make a $100 profit each weekend. SHOW ALL WORK.

Step-by-step explanation:

Given

Solving (a): Equation when profit = 100.

This implies that:

So, we have:

Rewrite as:

Solving (b): Calculate t, in (a)

In a, we have:

Expand

Factorize

Factor out t - 15

Split

Solve

The prices are $5 and $15, respectively

answer: the distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula