Word Problems and Modeling
A free Pre-Algebra lesson from the “Cumulative Review and Test Prep” unit, with a worked example and practice problems including step-by-step solutions.
Word problems become easier when you identify the unknown, choose a variable, and translate each phrase into math. After solving, check the answer in the story, not just in the equation. In Cumulative Review and Test Prep, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.
What you'll learn
- Translate words into expressions and equations
- Choose operations from context
- Check whether an answer makes sense
Worked example
Problem. A movie ticket costs 9 dollars. You buy a ticket and a snack. The total is 15 dollars. How much was the snack?
- Let s be the snack cost.
- Write 9 + s = 15.
- Subtract 9 from both sides: s = 6.
- Connect the calculation back to Word Problems and Modeling so the method, not just the arithmetic, is clear.
Answer: 6 dollars
Practice problems
1. A notebook costs 4 dollars and a pen costs 2 dollars. What is the total?
Show solution
- Warm-up: First identify exactly what the question is asking: A notebook costs 4 dollars and a pen costs 2 dollars. What is the total?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Add the two costs.
- 4 + 2 = 6.
- Check the result by substituting or estimating: the response should match 6 and make sense in the original problem.
Answer: 6
2. Mia has 18 cards and gives away 7. How many remain?
Show solution
- Warm-up: First identify exactly what the question is asking: Mia has 18 cards and gives away 7. How many remain?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Giving away means subtract.
- 18 - 7 = 11.
- Check the result by substituting or estimating: the response should match 11 and make sense in the original problem.
Answer: 11
3. The phrase '5 more than x' means...
Choices: x + 5 · x - 5 · 5x · x/5
Show solution
- Warm-up: First identify exactly what the question is asking: The phrase '5 more than x' means...
- For data questions, identify what each statistic measures before calculating so the result matches the question.
- More than means addition.
- 5 more than x is x + 5.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: x + 5
4. A class has 6 tables with 4 students at each table. How many students are there?
Show solution
- Core Practice: First identify exactly what the question is asking: A class has 6 tables with 4 students at each table. How many students are there?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Each table has 4 students.
- 6 x 4 = 24.
- Check the result by substituting or estimating: the response should match 24 and make sense in the original problem.
Answer: 24
5. A bill of 45 dollars is split equally among 5 people. How much does each person pay?
Show solution
- Core Practice: First identify exactly what the question is asking: A bill of 45 dollars is split equally among 5 people. How much does each person pay?
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- Split equally means divide.
- 45 divided by 5 equals 9.
- Check the result by substituting or estimating: the response should match 9 and make sense in the original problem.
Answer: 9
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