a bookstore is placing an order for new books and magazines each book costs 15$ and each magazine cost 5$ the store can spend at most $1,000 on these books and magazines additionally each book takes up 2 square feet of space and each magazine takes up 1 square feet of space. the store has only 50 square feet of display space avaiable for the new items the following system of inequalities can be used to determine possible combinations of books x and magazines y the store can order

Answer 1

To formulate the system of inequalities that represents the situation described, we need to account for both the budget constraint and the display space constraint. Let \( x \) represent the number of books and \( y \) represent the number of magazines.

Budget Constraint:

Each book costs $15 and each magazine costs $5. The total cost should not exceed $1,000. This can be written as:

\[ 15x + 5y \leq 1000 \]

Display Space Constraint:

Each book takes up 2 square feet and each magazine takes up 1 square foot. The total space used should not exceed 50 square feet. This can be formulated as:

\[ 2x + y \leq 50 \]

Non-negativity Constraints:

Since the number of books and magazines cannot be negative, we have:

\[ x \geq 0 \] \[ y \geq 0 \]

Summary of the System of Inequalities:

The complete system of inequalities that represents the constraints the bookstore faces can be expressed as:

1. \( 15x + 5y \leq 1000 \) (Budget constraint)
2. \( 2x + y \leq 50 \) (Space constraint)
3. \( x \geq 0 \) (Non-negativity for books)
4. \( y \geq 0 \) (Non-negativity for magazines)

This system can be used to determine the possible combinations of books \( x \) and magazines \( y \) that the store can order without exceeding either the budget or the display space limitations.