Question

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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

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

The equation that models this scenario, where b(x) is the revenue generated and x is the number of 50¢ price increases, is: b(x) = (3 + 0.5x)(38 - 4x)

The initial rental price per book is $3.

For every 50¢ increase in the rental price, the business loses 4 rentals a day.

Let x be the number of 50¢ price increases.

Now, let's express the rental price and the number of books rented as functions of x:

The new rental price after x increases would be 3+0.5x dollars per book.

The number of books rented out after x increases would be 38−4x books a day, considering the decrease in rentals due to the price increase.

Now, to find the revenue b(x), you multiply the price per book by the number of books rented:

b(x)=(price per book)×(number of books rented)

Substitute in the expressions we derived:

b(x)=(3+0.5x)(38−4x)

Answer 2

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

Explanation:

Let

b= revenue generated per day

x= is the number of $0.5 price increases.

b = price x quantity.................................... (1)

Let derive the price function for the model

price = $3 per book

However, assuming x number of price increase by $0.5, future price is given as :

price = (3+0.5x)........................................... (2)

quantity = 38 per day

For every x number of price $ 0.5 price jump, quantity reduces by 4. So the quantity at any given time is given by:

quantity = (38-4x)........................................(3)

Substituting into equation (1),

We have:

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