Question

Mary babysits for $4 per hour. She also works as a tutor for $7 per hour. She wants to make at least $65 dollars. She is only allowed to work 13 hours per week. Write and graph a system of inequalities to represent this situation.

Answer 1

inequalities are x + y ≤ 13 and 4x + 7y ≥ 65

Explanation:

Given: Mary babysits for $4 per hour. She also works as a tutor for $7 per hour. She wants to make at least $65 dollars. She is only allowed to work 13 hours per week.

We have to write and graph the system of inequalities to represent this situation.

Let she babysits for x hours per week

and she works as a tutor for y hours per week

Then given she is allowed to work for 13 hours per week.

this inequality is stated as x + y ≤ 13

Mary babysits for $4 per hour if she babysits for x hours then she get 4x

She also works as a tutor for $7 per hour if she teach for y hours then she get 7y

also, she wants to make at least $65 dollars.

Then, this inequality is represented as 4x + 7y ≥ 65

Plotting of this two inequality is represented as graph shown below.

Answer 2

Convert the task into an equation so that you can graph the situation:
According to the given information :

x+y≤13
7x+4y≥65
Here is the graph based on the equation
As you can see, to achieve set goal Mary can work 6 or 7 hours.