Question

Adam and Barb had a book sale over the weekend. Adam sold 4 hardcover books and ten paperbacks. Barb sold 5 hardcover books and 7 paperbacks for the same prices each. Adam sold $62 worth of books while Barb sold $61 worth. How much did they charge for hardcovers and how much for paperbacks?
What is your understanding of the problem

. What is being asked and what will answer the question? Do not just copy the problem! Mathematically what kind of problem is this?

What skill or concept did we learn in this unit which, when applied to this problem, will allow you to solve the problem?

Show the equations you’ll use to set up the problem.

Be sure to label or explain what your variables mean.

Show the math work to arrive at the answer.

Write your final answer. Be sure to make it clear which is hardcover and which is paperback.

Answer 1

Let x represent the price they charge hardcover book and let y represent the price they charge for a paperback book.

4x + 10y = 62 . . . . . (1)
5x + 7y = 61 . . . . . . (2)

(1) x 5 ⇒ 20x + 50y = 310 . . . . (3)
(2) x 4 ⇒ 20x + 28y = 244 . . . . (4)

(3) - (4) ⇒ 22y = 66
y = 66 / 22 = 3

4x + 10(3) = 62
4x = 62 - 30 = 32
x = 32 / 4 = 8

Therefore, the price for a hardcover book is $8 and the price for a paperback book is $3.