SOLUTION: A library is having a book sale to raise money. Hardcover books cost $4 each and paperback books cost $2 each. A person spends $26 for 8 books. How many hardcover books did she pur

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Question 1008107: A library is having a book sale to raise money. Hardcover books cost $4 each and paperback books cost $2 each. A person spends $26 for 8 books. How many hardcover books did she purchase?
Found 2 solutions by fractalier, ikleyn:
Answer by fractalier(6550)   (Show Source): You can put this solution on YOUR website!
Call the number of hardcover and paperback books, h and p.
Thus
h + p = 8 and the value equation is
4h + 2p = 26
Now multiply the top one by four and subtract from the second one...we get
4h + 2p = 26
-(4h + 4p = 32)
----------------
-2p = -6
p = 3 so that
h = 5
Answer by ikleyn(52782)   (Show Source): You can put this solution on YOUR website!
.
 x +  y = 8,    (1)

4x + 2y = 26,   (2)

where x and y are the numbers of hardcover and softcover books respectively.

To solve, multiply the equation (1) by 2 (both sides) and then distract it from the equation (2). You will get

4x - 2x = 26 - 16,   or

2x = 10,   or   x = 5 - the number of hardcover books purchased.

Then from the equation (1) you get y = 3.

Check. 4*x + 2*3 = 4*5 + 2*3 = 26. OK.


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