Inequality Word Problems

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📚 Part 1: Multiple Choice

1. A bakery sells at least 10 cupcakes a day. Let c = cupcakes sold. Which inequality matches this?

c > 10

c ≥ 10 (Correct Answer)

c < 10

c ≤ 10

2. A car rental allows drivers younger than 75 years old. Let a = driver's age. Which inequality describes allowed ages?

a ≤ 75 (Correct Answer)

a > 75

a < 75

a ≥ 75

3. A hiker plans to walk no more than 8 miles today. Let m = miles walked. Which inequality matches the plan?

m > 8

m ≥ 8

m < 8

m ≤ 8 (Correct Answer)

4. A food safety guideline recommends refrigerator temperatures be below 40°F. Let T = temperature. Which inequality shows this guideline?

T ≥ 40

T < 40 (Correct Answer)

T > 40

T ≤ 40

✏️ Part 2: Short Answers — Set up and solve each inequality

5. Sarah needs $300 to buy new equipment. She already has $120. Let x = additional dollars she must save. Write an inequality and solve for x.

x ≥ 300 - 120
x ≥ 180

Sarah must save at least $180.

6. A storage box can hold less than 50 pounds. Each item weighs 18 pounds. Let n = number of items. Write an inequality for n and state the greatest whole number of items that will fit.

18n < 50
n < 50/18
n < 2.78

The greatest whole number of items is 2.

7. Today's temperature is 79°F. The forecast says the high must be no higher than 85°F. Let x = allowed increase in degrees. Write and solve an inequality for x.

79 + x ≤ 85
x ≤ 6

The allowed increase in degrees is at most 6°F.

8. A charity has raised $170 and needs more than $500. Each ticket sale raises $15. Let t = number of additional tickets to sell. Write and solve an inequality, then give the smallest whole number of tickets needed. Graph the solution on a number line.

170 + 15t > 500
15t > 330
t > 22

The smallest whole number of tickets needed is 23.