The local library had a sale to get rid of books that were slightly damaged . it sold paperback books for $2.00 and hard-covered books for $5.00. the library raised $271 and sold 89 books. how many hard-cover books were sold?

Hi there!

We can set up a systems of equation from this situation.

paperback books : x
hard-covered books : y

They sold total of 89 books.
x + y = 89

The library raised $271.
2.00x + 5.00y = 271
which can be rewritten as...
2x + 5y = 271

So we got

x + y = 89
2x + 5y = 271

Using substitution method would be easier than elimination for this equations.
Since we have to find out the number of hard-covered books, let's get rid of x.
Make the first equation to be x = 89 - y.

x = 89 - y
2x + 5y = 271

2 (89 - y) + 5y = 271
178 - 2y + 5y = 271
3y = 93
y = 31

The library sold 31 hard-covered books.
Hope this helped! :)