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?
A. 50 books and 0 magazines
B. 20 books and 15 magazines
C. 10 books and 30 magazines
D. 40 books and 5 magazines

Answer 1

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

1. Budget Constraint: \( 15x + 5y \leq 1000 \)
2. Space Constraint: \( 2x + y \leq 50 \)

Now we will check each option:

Option A: 50 books and 0 magazines (x = 50, y = 0)

1. Budget: \( 15(50) + 5(0) = 750 \) (which is ≤ 1000) ✅
2. Space: \( 2(50) + 0 = 100 \) (which is > 50) ❌

Option B: 20 books and 15 magazines (x = 20, y = 15)

1. Budget: \( 15(20) + 5(15) = 300 + 75 = 375 \) (which is ≤ 1000) ✅
2. Space: \( 2(20) + 15 = 40 + 15 = 55 \) (which is > 50) ❌

Option C: 10 books and 30 magazines (x = 10, y = 30)

1. Budget: \( 15(10) + 5(30) = 150 + 150 = 300 \) (which is ≤ 1000) ✅
2. Space: \( 2(10) + 30 = 20 + 30 = 50 \) (which is ≤ 50) ✅

Option D: 40 books and 5 magazines (x = 40, y = 5)

1. Budget: \( 15(40) + 5(5) = 600 + 25 = 625 \) (which is ≤ 1000) ✅
2. Space: \( 2(40) + 5 = 80 + 5 = 85 \) (which is > 50) ❌

Based on the evaluations:

• Option A is not valid.
• Option B is not valid.
• Option C is valid.
• Option D is not valid.

Thus, the only combination that satisfies both constraints is:

C. 10 books and 30 magazines.