Question

Edith babysits for x hours a week after school at a job that pays $4 an hour. She has accepted a

job that pays $8 an hour as a library assistant working y hours a week. She will work both jobs.
She is able to work no more than 15 hours a week, due to school commitments. Edith wants to
earn at least $80 a week, working a combination of both jobs.
Write a system of inequalities that can be used to represent the situation.
Graph these inequalities on the set of axes.
Determine and state one combination of hours that will allow Edith to earn at least $80 per week
while working no more than 15 hours.

Answer 1

To represent the situation, we create a system of inequalities using the given information. We graph the inequalities to determine the possible combinations of hours for Edith to earn at least 80 per week while working no more than 15 hours.

Step-by-step explanation:

To represent the situation, we can create a system of inequalities using the given information. Let's say Edith babysits for x hours a week and works as a library assistant for y hours a week.

The first inequality is x ≤ 15, because Edith cannot work more than 15 hours a week due to school commitments.

The second inequality is 4x + 8y ≥ 80, because Edith wants to earn at least 80 a week. The left side of the equation represents the total earnings from babysitting ($4 per hour) and working as a library assistant ($8 per hour).

We can now graph these inequalities on a set of axes to determine the possible combinations of hours that will allow Edith to earn at least 80 per week while working no more than 15 hours.

Answer 2

x+y is less than or equal to 15
4x+8y is greater than or equal to 80
x is greater than 0
y is greater than 0