Question

The local library had a sale to get rid of the books that were slightly damaged it’s on paper back books for two dollars and hardcover books for five dollars each the library raised $271 and sold 89 bucks how many hardcover books were sold

Answer 1

The Local Library sold 31 hardcover books.

Explanation:

Let number of paper back books be 'x'.

Let number of hardcover books be 'y'.

Given:

Total number of books sold = 89

Now Total number of books sold is equal to sum of number of paper back books and number of hardcover books.

framing in equation form we get;

`x+y=89 \ \ \ \ \ equation \ 1`

Now Given:

Cost of each paper back books = $2

Cost of each hardcover books = $5

Total Amount raised by library = $271

Now We know that Total Amount raised by library is equal to Cost of each paper back books multiplied by number of paper back books plus Cost of each hardcover books multiplied number of hardcover books.

framing in equation form we get;

`2x+5y=271 \ \ \ \ equation \ 2`

Now Multiplying equation 1 by 2 we get;

`2(x+y)=89*2\\\\2x+2y = 178 \ \ \ \ equation \ 3`

Now Subtracting equation 3 from equation 2 we get;

`(2x+5y)-(2x+2y)=271-178\\\\2x+5y-2x-2y=93\\\\3y = 93\\\\y=(93)/(3)=31`

Substituting the value of y in equation 1 we get;

`x+y =89\\\\x+31=89\\\\x =89-31 = 58`

Hence The Local Library sold 58 paper back books and 31 hardcover books.