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aev [14]
3 years ago
8

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.
Mathematics
1 answer:
Arte-miy333 [17]3 years ago
3 0

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

<em>The prices are $5 and $15, respectively</em>

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