Question

Aaron is purchasing party hats and fake mustaches for an end-of-the-school-year party. He can spend at most $30. Fake mustaches cost $3 each, and party hats cost $2 each. If he must purchase a combination of at least 15 mustaches and party hats, which of the following systems of inequalities best models the relationship between the number of mustaches, m, and party hats, p, described above?

a) m + p ≥ 15, quad 3m + 2p ≤ 30

b) m + p ≤ 15, quad 3m + 2p ≥ 30

c) m - p ≥ 15, quad 3m + 2p ≤ 30

d) m + p ≥ 15, quad 3m - 2p ≤ 30

Answer 1

The system of inequalities that best models the relationship between the number of mustaches, m, and party hats, p, is a) m + p ≥ 15, 3m + 2p ≤ 30.

Step-by-step explanation:

The system of inequalities that best models the relationship between the number of mustaches, m, and party hats, p, is a) m + p ≥ 15, 3m + 2p ≤ 30.

Let's break it down:

The inequality m + p ≥ 15 represents the condition that Aaron must purchase at least 15 mustaches and party hats combined.

And the inequality 3m + 2p ≤ 30 reflects the fact that Aaron's spending on mustaches and party hats should not exceed $30.