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A thrift shop sells pre-owned hardcover books for $7 each and pre-owne

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A thrift shop sells pre-owned hardcover books for $7 each and pre-owne  [#permalink]

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New post 28 Mar 2018, 02:58
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  35% (medium)

Question Stats:

76% (01:57) correct 24% (02:44) wrong based on 33 sessions

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A thrift shop sells pre-owned hardcover books for $7 each and pre-owned paperback books for $5 each. A customer makes a purchase of both hardcover books and paperback books. Before taxes, the total purchase price of the books is $56. How many total books did the customer purchase?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

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Re: A thrift shop sells pre-owned hardcover books for $7 each and pre-owne  [#permalink]

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New post 29 Mar 2018, 17:20
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Bunuel wrote:
A thrift shop sells pre-owned hardcover books for $7 each and pre-owned paperback books for $5 each. A customer makes a purchase of both hardcover books and paperback books. Before taxes, the total purchase price of the books is $56. How many total books did the customer purchase?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11


Letting h = the number of hardcover books purchased and b = the number of paperback books purchased, we can create the equation:

7h + 5b = 56

5b = 56 - 7h

5b = 7(8 - h)

b = [7(8 - h)]/5

We see that in order for b to be an integer, 5 must divide 7(8 - h), so h must be either 8 or 3.

When h = 8, b = 0; but the question states that both hardcover and paperback books were purchased, so b cannot equal 0.

When h = 3, b = 7, so the total number of books the customer purchased is 10.

Answer: D
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Re: A thrift shop sells pre-owned hardcover books for $7 each and pre-owne  [#permalink]

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New post 28 Mar 2018, 04:28
Bunuel wrote:
A thrift shop sells pre-owned hardcover books for $7 each and pre-owned paperback books for $5 each. A customer makes a purchase of both hardcover books and paperback books. Before taxes, the total purchase price of the books is $56. How many total books did the customer purchase?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11



7a + 5b = 56

7(3) + 5(7) = 21+35 = 56

7+3 = 10

as both books are purchased 10
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Re: A thrift shop sells pre-owned hardcover books for $7 each and pre-owne   [#permalink] 28 Mar 2018, 04:28
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