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

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: hours spent house cleaning

y: hours spent at sales job

Inequality 1: x + y ≤ 10

Inequality 2: 5x + 8y ≥ $56

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: # of bags of soil

y: # of plants

Inequality 1: x + y ≥ 5

Inequality 2: 4x + 10y ≤ $100

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: # of candles

y: # of flower arrangements

Inequality 1: x + y ≤ 200

Inequality 2: 5x + 6y ≥ $500

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: # of advanced tickets sold

y: # of tickets sold at the door

Inequality 1: x + y ≤ 300

Inequality 2: 3x + 4y ≥ $500

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: # of pounds of hamburgers

y: # of pounds of chicken

Inequality 1: x ≥ 3

Inequality 2: 2x + 3y ≤ $30

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: # of bracelets sold

y: # of necklaces sold

Inequality 1: x + y ≤ 50

Inequality 2: 2x + 3y ≥ $100