Question

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.
$b(x) = \square x^2 + \square x + \square$
reset next

Explanation:

Step1: Define price per book

Price per book after $x$ increases: $3 + 0.5x$

Step2: Define number of rentals

Number of rentals after $x$ increases: $38 - 4x$

Step3: Expand revenue formula

Revenue $b(x) = (3 + 0.5x)(38 - 4x)$
$= 3*38 + 3*(-4x) + 0.5x*38 + 0.5x*(-4x)$
$= 114 - 12x + 19x - 2x^2$

Step4: Simplify the expression

Combine like terms: $b(x) = -2x^2 + 7x + 114$

Answer:

$b(x) = -2x^2 + 7x + 114$
The filled boxes are: 2, 7, 114