Question

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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?

Answer 1

For this case we propose a system of equations:

a: Let the variable representing the cost of hardcover books

b: Let the variable representing the cost of paperback books

According to the statement data we have:

`5a + 4b = 100\\b = a-2`

Substituting the second equation into the first we have:

`5a+4(a-2)=100\\5a+4a-8=100\\9a=100+8\\9a=108\\a=(108)/(9)\\a=12`

Thus, the cost of hardcover books is $12

ANswer:

The cost of hardcover books is $12