Inequalities & Word Problems

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

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

Daniel can spend no more than $40 at the fair. If admission into the fair is $10 and the rides cost $1.50 each, which inequality represents the greatest number of rides Daniel can go on?

• 10x + 1.50 ≥ 40
• 1.50x + 10 ≤ 40
• 1.50x + 10 <40
• 10x + 1.50 < 40

A willow tree is 5.1 feet tall and grows at a rate of 2.5 feet a year. After how many years will the tree have reached no more than 60 feet tall?

• 5.1 + 2.5y ≥ 60
• 60 < 5.1 + 2.5
• 5.1 + 2.5y ≤ 60
• 5.1 + 2.5y > 60

Four times a number increased by  7 is at least 19. 

• 4x > 19
• 4x + 7 ≥ 19
• 4x < 19
• 4x + 7 ≤ 19

Which sentence represents m > 41?

• Mary’s points, m, totaled more than 41
• Calvin ran no less than 41 miles, m
• The temperature, m, was less than 41°F
• The magazines’ cost, m, was not more than $41.

Erin can read at least 80 words per minute. Write an inequality to show this situation. 

• x > 80
• x < 80
• x ≥ 80
• x ≤ 80