Question

Carla makes $12 per hour babysitting and $7 per hour gardening. She wants to make more than $90 per week but can only work a maximum of 15 hours in a week. Write a system of inequalities to describe this situation

Answer 1

To describe Carla's situation, we can create a system of inequalities based on the given information.

Let's assign variables to represent the number of hours Carla spends babysitting and gardening in a week. Let's use "b" for babysitting hours and "g" for gardening hours.

The inequalities can be written as follows:

1. Carla wants to make more than $90 per week:

12b + 7g > 90

This inequality represents the total amount of money Carla earns in a week by multiplying the hourly rate for babysitting (12) by the number of hours spent babysitting (b), adding it to the product of the hourly rate for gardening (7) and the number of hours spent gardening (g), and setting it to be greater than 90.

2. Carla can only work a maximum of 15 hours in a week:

b + g ≤ 15

This inequality represents the total number of hours Carla can work in a week by adding the number of hours spent babysitting (b) and the number of hours spent gardening (g), and setting it to be less than or equal to 15.

So, the system of inequalities that describes Carla's situation is:

12b + 7g > 90

b + g ≤ 15

These inequalities ensure that Carla earns more than $90 per week while working a maximum of 15 hours