Writing and Solving Inequalities Word Problems (A) - The Amusement Park

Q: How is the answer key formatted for these problems?

Each problem shows the inequality, the solution range for the variable, and a short sentence interpreting what the inequality means in the situation.

Sep 23, 2026

Uploaded by Jordan Avery

Worksheet focused on writing and solving inequality word problems set in an amusement park context. Each item asks students to translate real situations into inequalities, solve for a variable as a range of values, and interpret results in context. Topics include height limits for a roller coaster, budgeting for ride tickets, earning prize points, remaining waiting time, saving for souvenirs, total weight limits for riders, weekly earning goals, and an admission plus per-ride cost challenge with an answer key.

LanguageEnglish

CategoryExam

FormatPDF

Pages4

Reading Time10 min

AccessFree to download

Directions

Inequality Word Problems

Problems 1-7

Challenge Problem 8

Answer Key

Name: ______________________________________ Writing and Solving Inequalities Word Problems (A) THE AMUSEMENT PARK Directions: For each problem: write an inequality, solve it, and interpret the solution in context. Remember: Inequality key words: at least ≥, at most ≤, more than >, fewer/less than < . Solve like an equation—but keep the inequality symbol. The solution is a range of values, not just one number. 1. You must be at least 48 inches tall to ride the roller coaster. You are currently 42 inches tall. Write and solve an inequality for the number of inches g you still need to grow. Inequality: Solution: What this means: 2. A family wants to spend at most $120 on ride tickets. Each ticket costs $8. Write and solve an inequality for the number of tickets t they can buy. Inequality: Solution: What this means: 3. A game awards prizes if you score more than 50 points. You already have 32 points. Write and solve an inequality for the additional points p you need. Inequality: Solution: What this means: Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) 4. You have already waited 12 minutes in line. The total wait time is less than 30 minutes. Write and solve an inequality for the additional time m you could still wait. Inequality: Solution: What this means: 5. A souvenir costs at least $15. You have saved $9. Write and solve an inequality for the additional amount a you still need to save. Inequality: Solution: What this means: 6. A roller coaster car holds at most 480 pounds total. Two friends weigh 145 lb and 130 lb. Write and solve an inequality for the weight p of a third friend who could ride. Inequality: Solution: __________________________ What this means: 7. A park employee earns $11 per hour and wants to earn more than $132 this week. Write and solve an inequality for the hours h she must work. Inequality: Solution: __________________________ What this means: Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) Challenge Problem 8. An amusement park charges $18 admission plus $3 per ride. You have $45 total. Write and solve an inequality for the number of rides r you can go on. Inequality: Show your work: Solution: __________________________ What this means: Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com) ANSWER KEY 1.) 1. ) 42 + g ≥ 48 → Solution: g ≥ 6 | You must grow at least 6 more inches. 2.) 2. ) 8t ≤ 120 → Solution: t ≤ 15 | The family can buy at most 15 tickets. 3.) 3. ) 32 + p > 50 → Solution: p > 18 | You need more than 18 additional points. 4.) 4. ) 12 + m < 30 → Solution: m < 18 | You can wait fewer than 18 more minutes. 5.) 5. ) 9 + a ≥ 15 → Solution: a ≥ 6 | You need to save at least $6 more. 6.) 6. ) 145 + 130 + p ≤ 480 → Solution: p ≤ 205 | The third friend must weigh at most 205 pounds. 7.) 7. ) 11h > 132 → Solution: h > 12 | She must work more than 12 hours. 8.) 8. ) 18 + 3r ≤ 45 → Solution: r ≤ 9 | You can go on at most 9 rides. Mashup Math LLC | Al[l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com](l Rights Reserved | Get More K-12 Math Worksheets at www.mashupmath.com)

FAQs

What do you do for each inequality word problem on this worksheet?

Write an inequality, solve it, and interpret the solution in context. The solution is a range of values, not just one number.

Which inequality words and symbols are emphasized in the directions?

The worksheet highlights at least (≥), at most (≤), more than (>), and fewer/less than (<).

How is the answer key formatted for these problems?

Each problem shows the inequality, the solution range for the variable, and a short sentence interpreting what the inequality means in the situation.

Sep 23, 2026

Uploaded by Jordan Avery