Question

Ms. Kirk, the head librarian at the Harrison County Library, can spend at most $3,700 to expand the children's section of the library. When she buys from a particular discount seller, paperback books cost $2 each and hardback books cost $18 each.
Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of paperback books
y = the number of hardback books

Answer 1

To express the budget constraints for the children's section of the library, we can set up an inequality based on the cost of the books.

Given:
- The cost of paperback books is $2 each.
- The cost of hardback books is $18 each.
- Ms. Kirk can spend at most $3,700.

We can translate this information into an inequality using the variables defined:
- Let \( x \) be the number of paperback books.
- Let \( y \) be the number of hardback books.

The total cost for purchasing \( x \) paperback books and \( y \) hardback books is \( 2x + 18y \). The inequality representing the maximum amount Ms. Kirk can spend is:

\[
2x + 18y \leq 3700
\]

To put this inequality in standard form, we can rearrange it:

1. We write it as:
\[
2x + 18y - 3700 \leq 0
\]

2. To make it more conventional, we can express it as:
\[
2x + 18y \leq 3700
\]

Thus, the inequality in standard form that describes this situation is:

\[
2x + 18y \leq 3700
\]