Inequality Word Problems: Context and Combining Terms

1. Sarah has twice as many marbles as Tom. If Tom has x marbles, write an inequality to represent the situation if Sarah has at least 10 marbles. Solve for x and interpret the solution in context.

• x > 10

• x < 5

• x = 7

• x >= 5

Tags

CCSS.6.EE.B.8

2. A concert hall can hold a maximum of 500 people. If tickets are sold for $15 each and the cost of organizing the concert is $2000, write an inequality to find the minimum number of tickets that must be sold to break even. Solve and interpret the result.

• 300

• 200

• 450

• 134

3. A store sells pencils for $0.50 each and erasers for $0.75 each. If a student spends no more than $10, write an inequality to represent the number of pencils (p) and erasers (e) they can buy. Solve for e in terms of p and interpret the solution.

• e ≤ (40/3) - (2/3)p

• e ≤ 15 - 0.75p

• e ≤ 10 - p

• e ≤ 20 - 0.5p

4. A gardener has 30 feet of fencing to create a rectangular garden. If the length is represented by x and the width by y, write an inequality for the perimeter and solve for y in terms of x. Interpret the solution in the context of the garden's dimensions.

• y ≥ 15 - x

• y = 30 - x

• y < 15 - x

• y ≤ 15 - x

5. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer wants to spend no more than $100, write an inequality to represent the miles driven (m). Solve for m and interpret the solution in context.

• m ≤ 300

• m ≤ 250

• m ≤ 150

• m ≤ 200

6. A school is planning a field trip and has a budget of $1200. If each student pays $30 and there are x students, write an inequality to represent the maximum number of students that can attend. Solve for x and interpret the solution in context.

• x ≤ 40

• x ≤ 20

• x ≤ 50

• x ≤ 30

7. A recipe requires 2 cups of flour and 3 cups of sugar. If you have x cups of flour and y cups of sugar, write an inequality to represent the situation if you want to make at least 5 batches of the recipe. Solve for y in terms of x and interpret the solution.

• y <= 20

• y = 12

• y >= 15

• y >= 10

8. A bike shop sells bikes for $200 each and helmets for $50 each. If a customer wants to spend no more than $1000, write an inequality to represent the number of bikes (b) and helmets (h) they can buy. Solve for h in terms of b and interpret the solution.

• h ≤ 20 - 4b

• h ≤ 15 - 3b

• h ≤ 10 - 2b

• h ≤ 25 - 5b

9. A local charity is collecting cans for a food drive. If they need at least 200 cans and each person can donate x cans, write an inequality to represent the number of people (p) needed to meet the goal. Solve for p in terms of x and interpret the solution.

• p <= 200 / x

• p = 200 * x

• p >= 200 / x

• p < 200 / x

Tags

CCSS.6.EE.B.8

10. A student is saving money for a new laptop that costs $800. If they save $50 each week and already have x dollars saved, write an inequality to represent how many weeks (w) it will take to reach the goal. Solve for w in terms of x and interpret the solution.

• w <= (800 - x) / 50

• w >= (800 - x) / 50

• w < (800 - x) / 50

• w = (800 + x) / 50