Question

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.

Answer 1

Answer:

$(a)\ t^2 - 20t + 75= 0$

$(b)$ $t = 5; t -=15$

Step-by-step explanation:

Given

$p(t) = t^2 - 20t + 175$

Solving (a): Equation when profit = 100.

This implies that:

$p(t) =100$

So, we have:

$100 = t^2 - 20t + 175$

Rewrite as:

$t^2 - 20t + 175 - 100 = 0$

$t^2 - 20t + 75= 0$

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

In a, we have:

$t^2 - 20t + 75= 0$

Expand

$t^2 - 15t -5t + 75= 0$

Factorize

$t(t - 15) -5(t - 15)= 0$

Factor out t - 15

$(t - 5)(t - 15)= 0$

Split

$t - 5 = 0; t - 15 =0$

Solve

$t = 5; t -=15$

The prices are $5 and $15, respectively