Question

A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per hour for gardening. Because he is still in school, he is only allowed to work for at most 20 hours per week. His goal is to make at least $300 per week.

a. Create a system of equations or inequalities that models the situation. Define the variables you use.

Answer 1

To model the situation, use the variables x and y to represent the number of hours spent mowing lawns and gardening, respectively. The constraints are x + y <= 20 (maximum hours per week) and 15x + 20y >= 300 (minimum earnings per week).

Step-by-step explanation:

To create a system of equations or inequalities that models the situation, we can define the two variables:

x = number of hours spent mowing lawns

y = number of hours spent gardening

The student can work for at most 20 hours per week, so we have the constraint:

x + y <= 20

The student wants to make at least $300 per week, so we have the inequality:

15x + 20y >= 300

These two equations/inequalities model the situation.

Variables: x, y

System of equations/inequalities:

x + y <= 20

15x + 20y >= 300