Question

A wholesaler purchased a certain number of books for $864. If the price per book was $3 less, the number of the books that could be purchased for $864 would be 4 more. How much did each book cost originally?

Answer 1

$27

Explanation:

b will be the number of books and p will be the price, now we just use a system of equations

bp = 864

b=864/p

(b+4)(p-3) = 864

(864/p +4)(p-3) = 864

864 - 2592/p + 4p -12 = 864

864p - 2592 + 4p^2 -12p - 864p = 0

4p^2 -12p -2592 = 0

4(p^2 - 3p -648) = 0

4((p - 3/2)^2 - 2601/4) = 0 (completed the square here)

4(p - 3/2)^2 -2601 = 0

p = +/-51/2+3/2

p = 27 or -24

A negative price doesn't make sense so it's 27, now we go back to the other equation if you want to find the number of books.

b=864/p

b = 864/27

b = 32