Question

Charlie runs a book rental business. He currently charges $3 per book and rents out an average of 38 books a day. According to a study, for every 50¢ increase in rental price, the average business can expect to lose 4 rentals a day. Complete the equation that models this scenario, where b(x) is the revenue generated and x is the number of 50¢ price increases.

Answer 1

Answer:

The equation that models this scenario $b(x)=(3+0.5x)(38-4x)$

Step-by-step explanation:

First we convert 50 cent into dollar,

1 cent =$\frac{1}{100}$ dollar

1 cent = 0.01 dollar

50 cent = 0.5 dollar

According to question,

x is the number of 50¢=$0.5 price increases.

b(x) is the revenue generated

He currently charges $3 per book.

i.e. price of book = 3+0.5x

Quantity or average = 38 per day

According to a study, for every 50¢ increase in rental price, the average business can expect to lose 4 rentals a day.

i.e. quantity became 38-4x

Revenue = Price × Quantity

The required equation is given by,

$b(x)=(3+0.5x)(38-4x)$