Writing Inequalities

Joan needed $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?

• 5x + 10 ≥ 100
• 5x - 100 ≥ 10
• 10x + 5 ≤ 100
• 5x + 10 > 100

Camie and Jorge each begin saving money for a new computer. Camie saves $5 per week plus $50 she receives for her birthday. Jorge saves $7 per week. Which of the following can be used to find w, the number of weeks until Jorge has saved at least the same amount as Camie?

• 7w = 5w+50

• 50+5w < 7w

• 5w+50 ≥ 7w

• 7w ≥ 5w+50

Joe’s Canoes charges an initial fee of $20 plus $4 an hour. Callie’s Canoes charges a flat rate of $14 an hour. Find the number of hours for which the total amount that both places charge would be the same.

• 3 hours
• 4 hours
• 1 hour
• 2 hours

A caterer charges a service fee and a food fee, with the total being less than $1,000. The service fee is $175. Which inequality can be used to determine the food fee?

• x + 175 ≤ 1000

• x − 175 < 1000

• x + 175 < 1000

• x − 175 ≤ 1000

Keith is saving money for a new digital camera with his seasonal job. He will work the next 8 weeks he needs to earn at least $250. Which inequality can be used to find how much money Keith needs to earn each week?

• x + 8 ≥ 250

• 8x ≥ 250

• x + 8 ≤ 250

• 8x ≤ 250

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Your brother has $2,000 saved for a vacation. His airplane ticket is $637. Which inequality can be used to find out how much he can spend on everything else?

• 637 + x ≤ 2000

• x − 637 ≤ 2000

• 637 + x ≥ 2000

• x − 637 < 2000

Your coach said to spend no less than 45 minutes practicing each day. You spent 14 minutes practicing this morning. How many more minutes do you have to practice for?

• 14x ≥ 45

• x + 14 ≤ 45

• 14x ≤ 45

• x + 14 ≥ 45

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 wants to keep the total cost under $600. Which inequality represents the maximum amount of hours the DJ will play at the dance?

• 125x + 55 ≤ 600
• 125x + 55 ≥ 600
• 125x + 55 > 600
• 125x + 55 < 600

Cody’s Gym charges a $15 fee to join and $30 per month. Tyler’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 Tyler’s gym would be a better deal.

• 30 + 20x < 15 + 30x
• 30x + 20 < 15x + 30
• 30 + 20x > 15 + 30x
• 30x + 20 > 15x + 30