A bookstore is placing an order for new books and magazines. Each book costs $15, and each magazine costs $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 foot of space. The store has only 50 square feet of display space available 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: 15x+5y≤1000 2x+y≤50 Which combinations of books, x, and magazines, y, can the bookstore order? (1 point) Responses 20 books and 15 magazines 20 books and 15 magazines 50 books and 0 magazines 50 books and 0 magazines 40 books and 5 magazines 40 books and 5 magazines 10 books and 30 magazines

Answer 1

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

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

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

Let's evaluate each option individually:

1. 20 books and 15 magazines:

   • Budget: \( 15(20) + 5(15) = 300 + 75 = 375 \leq 1000 \) (satisfied)
   • Space: \( 2(20) + 15 = 40 + 15 = 55 \leq 50 \) (not satisfied)

2. 50 books and 0 magazines:

   • Budget: \( 15(50) + 5(0) = 750 + 0 = 750 \leq 1000 \) (satisfied)
   • Space: \( 2(50) + 0 = 100 + 0 = 100 \leq 50 \) (not satisfied)

3. 40 books and 5 magazines:

   • Budget: \( 15(40) + 5(5) = 600 + 25 = 625 \leq 1000 \) (satisfied)
   • Space: \( 2(40) + 5 = 80 + 5 = 85 \leq 50 \) (not satisfied)

4. 10 books and 30 magazines:

   • Budget: \( 15(10) + 5(30) = 150 + 150 = 300 \leq 1000 \) (satisfied)
   • Space: \( 2(10) + 30 = 20 + 30 = 50 \leq 50 \) (satisfied)

The only combination that satisfies both constraints is 10 books and 30 magazines.

Thus, the valid option is 10 books and 30 magazines.