A bookstore is placing an order for new books and magazines. Each book calls $15 and H magazine cost 5. The store can spend at most $1000 on these books and magazines. Additionally, each book takes up 2 square feet of space and each magazine takes up one square foot of space. The store has only 50 square feet of display space available for their new items. The following system of inquiries can be used to determine possible combinations. A book's x and magazine's why the store can order

Question

15x + 5y \leq 1000
2x + y \leq 50
Which combination of books and magazines y candy bookstore order

Fifty books in zero magazines forty books and five magazines ten books in thirty magazines twenty books and fifteen magazines

Answer 1

To determine which combinations of books (\( x \)) and magazines (\( y \)) the bookstore can order, we need to analyze the inequalities given:

1. Budget constraint: \[ 15x + 5y \leq 1000 \]

2. Space constraint: \[ 2x + y \leq 50 \]

We'll check each combination provided:

1. 50 books and 0 magazines (\( x = 50, y = 0 \)):

   • Budget: \( 15(50) + 5(0) = 750 \) (satisfies budget)
   • Space: \( 2(50) + 0 = 100 \) (exceeds space)
   • Not valid.

2. 40 books and 5 magazines (\( x = 40, y = 5 \)):

   • Budget: \( 15(40) + 5(5) = 600 + 25 = 625 \) (satisfies budget)
   • Space: \( 2(40) + 5 = 80 + 5 = 85 \) (exceeds space)
   • Not valid.

3. 10 books and 30 magazines (\( x = 10, y = 30 \)):

   • Budget: \( 15(10) + 5(30) = 150 + 150 = 300 \) (satisfies budget)
   • Space: \( 2(10) + 30 = 20 + 30 = 50 \) (satisfies space exactly)
   • Valid.

4. 20 books and 15 magazines (\( x = 20, y = 15 \)):

   • Budget: \( 15(20) + 5(15) = 300 + 75 = 375 \) (satisfies budget)
   • Space: \( 2(20) + 15 = 40 + 15 = 55 \) (exceeds space)
   • Not valid.

Based on the evaluations above, the only valid combination of books and magazines that the bookstore can order is:

10 books and 30 magazines.