How would you solve these inequalities?

Question

1. You can work a total of no more than 10 hours each week at your two jobs. House

cleaning pays $5 per hour and your sales job pays $8 per hour. You need to earn at

least $56 each week to pay your bills. Write a system of inequalities that shows the

various numbers of hours you can work at each job.

x:

y:

Inequality 1:

Inequality 2:

2. Katie is buying plants and soil for her garden. The soil cost $4 per bag, and the

plants cost $10 each. She wants to buy at least 5 plants. She cannot spend more than

$100. Write and graph a system of linear inequalities to model all possible solutions to

the situation.

x:

y:

Inequality 1:

Inequality 2:

3. The girls’ swim team is hosting a fundraiser. They would like to raise at least $500.

They are selling candles for $5 and flower arrangements for $6. The girls estimate that

at most they will sell 200 items. Write a system of inequalities to represent this

situation.

x:

y:

Inequality 1:

Inequality 2:

4. The ninth graders are hosting the next school dance. They would like to make at

least a $500 profit from selling tickets. The ninth graders estimate that at most 300

students will attend the dance. They will earn $3 for each ticket purchased in advance

and $4 for each ticket purchased at the door. Write a system of inequalities to

represent this situation.

x:

y:

Inequality 1:

Inequality 2:

5. In order to prepare for your summer bash, you go to the supermarket to buy

hamburgers and chicken. Hamburgers cost $2 per pound and chicken costs $3 per

pound. You have no more than $30 to spend. You expect to purchase at least 3

pounds of hamburgers.

x:

y:

Inequality 1:

Inequality 2:

6. Jenny is making jewelry for an Arts and Crafts show. She would like to make at

least $100 in sales. She estimates that she will sell at most 50 pieces of jewelry. The

bracelets that she is selling cost $2 and the necklaces cost $3.

x:

y:

Inequality 1:

Inequality 2:

Answer 1

I'll do #1 for you, but you need to try the rest on your own. Tutors are here to help show you how to do problems, but we're not here to do all of your homework for you.

Let x be the number of hours you work at the cleaning job

Let y be the number of hours you work at the sales job

You can work no more than 10 hours per week: x + y ≤ 10

You need to earn at least $56 per week: $5x + $8y ≥ $56

Answer 2

5*5+8*5=65

5*4+8*5=60

5*3+8*5=55