Inequality Practical Problems

Which inequality represents:4 more than a number is at most twice the number

• 4+ x ≥ 2x

• 4x ≤ 4 + 2x

• 4 + x < 2x

• 4 + x ≤ 2x

Jack’s Gym charges a $15 fee to join and $30 per month. Tim’s Gym charges a $30 fee to join and $20 per month. Write an inequality that could be used to determine after how many months Tim’s gym would be cheaper than Jack's gym.

The Penny store installs carpet for $80 plus $9.50 per square yard of carpet. The Carpet Mall charges $120 for installation and $7.50 per square yard of carpet. Write an inequality that could be used to determine the number of square yards of carpet that need to be installed for The Penny Store to charge more than The Carpet Mall.

The school band is selling concert tickets for a fundraiser. Sara sold some tickets. Tom sold twice as many tickets as Sara. Together, Sara and Tom sold more than 90 tickets. What is the least amount of tickets that Sara could have sold?

• 31

• 40

• 45

• 46

Tyrod needs at least $820 to buy the computer he wants. He has already saved $330. He earns $50 per lawn that he cuts. What is the least number of lawns that he can cut and buy the computer? Which inequality represents the problem?(**Write the answer down, because you will need it to solve the next question)

• 50x - 330 ≥ 820

• 50x - 330 ≤ 820

• 50x + 330 ≥ 820

• 50x + 330 ≤ 820

Beth is going to the State Fair which costs $10 to get in. Each ride costs $5. If she has $45 to spend at the Fair, what is the greatest number of rides she can ride?

Which inequality represents the problem?(**Write the answer down, because you will need it to answer the next question)

Troy's class is going to the National Aquarium for a field trip. The group cost is $600. This will cover the cost of admission and lunch for each student. The 20 students have already raised $280. Which inequality represents the least amount of money each student will need to raise to go to the Aquarium?

The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour in addition to $55 for an assistant. The committee can spend at most $680. Which inequality represents the maximum amount of hours the DJ will play at the dance?

• 125x + 55 ≤ 680

• 125x + 55 ≥ 680

• 125x + 55 > 680

• 125x + 55 < 680

The Starbucks Company wants to send a team of three representatives to a conference.  Their budget is $700 plus $125 per day for expenses.  If their total budget cannot exceed $1,400.00, which of the following inequalities expresses this situation?

• 125x + 700 ≥1400

• 700 + 125x ≤1400

• 700x + 125 ≤1400

• 125x - 700 ≤ 1400

Joan needs more than $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn. Which inequality represents the minimum amount of hours she will need to babysit in order for her to buy her calculator?

• x<18

• x>22

• x<22

• x>18