Question

Ms. Mendoza, the head librarian at the Shelby County Library, can spend at most $4,900 to expand the children's section of the library. When she buys from a particular discount seller, paperback books cost $1.70 each and hardback books cost $17.89 each.
Write 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 formulate the inequality describing the situation, we need to account for the costs of the paperback and hardback books in relation to the budget that Ms. Mendoza has available.

Given:
- The cost of a paperback book is $1.70.
- The cost of a hardback book is $17.89.
- The maximum budget available is $4,900.

Let \( x \) be the number of paperback books, and \( y \) be the number of hardback books.

The total cost for buying \( x \) paperback books and \( y \) hardback books can be expressed as:

\[
1.70x + 17.89y
\]

Since Ms. Mendoza can spend at most $4,900, we can set up the following inequality:

\[
1.70x + 17.89y \leq 4900
\]

To convert this into standard form, we can eliminate the decimals by multiplying the entire inequality by 100:

\[
170x + 1789y \leq 490000
\]

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

\[
170x + 1789y \leq 490000
\]