Question

Josh is an avid reader. His generous grandparents gave him money for the holidays, and he decided to spend at most $120 on books. Books R' Us is running a special: all paperback books are $5.00, and hardback books are $10.00. Josh wants to purchase at least 15 books. Which of the following systems of inequalities correctly represents the given constraints?

a. 5x + 10y = 120 and x + y ≥ 15
b. 5x + 10y > 120 and x + y = 15
c. 5x + 10y ≥ 120 and x + y ≤ 15
d. 5x + 10y ≤ 120 and x + y ≥ 15

Answer 1

The following systems of inequalities correctly represents the given constraints: d. 5x + 10y ≤ 120 and x + y ≥ 15

Step-by-step explanation:

The given constraints state that Josh has a maximum spending limit of $120 and wants to purchase at least 15 books. Let x represent the number of paperback books and y represent the number of hardback books.

The first inequality, 5x + 10y ≤ 120, represents the total spending limit. Since each paperback book costs $5.00 and each hardback book costs $10.00, the total spending is 5x + 10y. The inequality ≤ indicates that the total spending cannot exceed $120.

The second inequality, x + y ≥ 15, represents the minimum number of books Josh wants to purchase. The sum of paperback and hardback books, x + y, must be at least 15.

Therefore, the system of inequalities 5x + 10y ≤ 120 and x + y ≥ 15 correctly represents the given constraints.

Options a, b, and c are incorrect because they either have an incorrect inequality sign or do not represent both constraints simultaneously.