Question

A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per hour for gardening. If he is only allowed to work for at most 20 hours per week and his goal is to make at least $300 per week, which of the following represents the inequality for this situation?

A) 15x + 20y ≥ 300
B) 15x + 20y ≤ 300
C) 15x + 20y = 300
D) 15x - 20y ≥ 300

Answer 1

The correct inequality that represents the situation is A) 15x + 20y ≥ 300. The student charges $15 per hour for mowing lawns and $20 per hour for gardening. His goal is to make at least $300 per week and work for at most 20 hours per week.

Step-by-step explanation:

The correct inequality that represents the situation is A) 15x + 20y ≥ 300

To understand why, let's break down the problem. The student charges $15 per hour for mowing lawns and $20 per hour for gardening. Let's assume he works x hours mowing lawns and y hours gardening.

The total income he earns can be calculated as 15x + 20y. Since his goal is to make at least $300 per week, the inequality becomes 15x + 20y ≥ 300.

Furthermore, the student is only allowed to work for at most 20 hours per week. This constraint can be represented as x + y ≤ 20.

So the correct inequality for the situation is A) 15x + 20y ≥ 300.