SOLUTION: Miguel spends $100 on books, five of which are hardcover and the remaining four are paperback. The prices at the bookstore are based on whether the book is hardcover or paperback.

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Question 1204487: Miguel spends $100 on books, five of which are hardcover and the remaining four are paperback. The prices at the bookstore are based on whether the book is hardcover or paperback. It charges $2 less for paperback books than for hardcover books. What is the price for hardcover books?
Found 4 solutions by mananth, Theo, josgarithmetic, greenestamps:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
Miguel spends $100 on books, five of which are hardcover and the remaining four are paperback. The prices at the bookstore are based on whether the book is hardcover or paperback. It charges $2 less for paperback books than for hardcover books. What is the price for hardcover books?
let price of hardcover book be $x Number of books purchased = 5

Price for paperback will be$ (x-2) Number of books purchased = 4
Miguel spends $100 on book
5x+4(x-2) =100
5x+4x-8=100
9x = 108
x= 12
The price of a hardcover book is $12.



Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
price for a hardcover book is x.
price for a paperback book is x - 2
total spent is 100.
equation is 5 * x + 4 * (x - 2) = 100
simplify to get 5 * x + 4 * x - 8 = 100
combine like terms to get 9 * x - 8 = 100
add 8 to both sides of the equation to get 9 * x = 108
divide both sides of the equation by 9 to get x = 108 / 9
solve for x to get x = 12.
5 * x + 4 * (x - 2) = 100 becomes 5 * 12 + 4 * 10 = 100 which becomes 60 + 40 = 100 which becomes 100 = 100, confirming the value of x is good.
your solution is:
the price of a hardcover book is 12.
the price of a paperback book is 10.
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
                  PRICE       QTY.       COST

HARDCOV             h          5         5h

PAPERB             h-2         4       4(h-2)

Total                                    100

If this table of data is understood then you know what to do.

Think carefully about the COST column and you could see
and then showing an obvious multiple of 9.
.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Presumably a formal algebraic solution was wanted, but you can get good mental exercise solving the problem informally, using logical reasoning and simple mental arithmetic.

The five hardbound books each cost $2 more than each paperback. That's 5 times $2 or $10 "extra" for the hardbound books.

What is then left is nine books each with the same price, costing a total of $100-$10 = $90. That's $90/9 = $10 per book.

So the paperback books cost $10 each, and the hardbound books each cost $2 more than that.

ANSWER: $12 for each hardbound book.
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