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:

Question

15x+5y≤1000

2x+y≤50

Which combinations of books, x, and magazines, y, can the bookstore order?

(1 point)
Responses

40 books and 5 magazines
40 books and 5 magazines

20 books and 15 magazines
20 books and 15 magazines

50 books and 0 magazines
50 books and 0 magazines

10 books and 30 magazines

GPT-4o mini · Answer

To determine which combinations of books (x) and magazines (y) the bookstore can order based on the given system of inequalities, we will evaluate each option against the inequalities:

Total cost constraint: $15x + 5y \leq 1000$
Space constraint: $2x + y \leq 50$

Now, let's evaluate each option:

40 books and 5 magazines:
- Cost: $15(40) + 5(5) = 600 + 25 = 625$ (within budget)
- Space: $2(40) + 5 = 80 + 5 = 85$ (exceeds available space)
20 books and 15 magazines:
- Cost: $15(20) + 5(15) = 300 + 75 = 375$ (within budget)
- Space: $2(20) + 15 = 40 + 15 = 55$ (exceeds available space)
50 books and 0 magazines:
- Cost: $15(50) + 5(0) = 750 + 0 = 750$ (within budget)
- Space: $2(50) + 0 = 100 + 0 = 100$ (exceeds available space)
10 books and 30 magazines:
- Cost: $15(10) + 5(30) = 150 + 150 = 300$ (within budget)
- Space: $2(10) + 30 = 20 + 30 = 50$ (exactly meets available space)

Based on the evaluations:

40 books and 5 magazines: does not satisfy space
20 books and 15 magazines: does not satisfy space
50 books and 0 magazines: does not satisfy space
10 books and 30 magazines: satisfies both constraints

The only feasible combination from the options provided is 10 books and 30 magazines.