Answer:
Step-by-step explanation:
Let x = the number of 50-cent increases in the cost of a book rental.
Right now he is renting 38 books per day at $3 per rental. If he raises his price he will lose 4 rentals per increase. The money part of this is:
$3 + .5x = the price per book rental after the increase. That's how much money he will make. The money made is NOT the same thing as the number of rentals. Therefore, they are put into separate expressions.
The number of rentals is:
38 - 4x. This is the number of books he is currently renting minus the number of book rentals he will lose per price increase. Putting those 2 expressions together and multiplying them will give you the end result of this increase in price.
(3 + .5x)(38 - 4x) = 114 - 12x + 19x - 2x², or putting it in descending powers of x and combining like terms:
-2x² + 7x + 114
