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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

Why it matters: Every real problem starts as words, not equations. Translating the situation into an expression or equation is the Pre-Algebra skill that shows up most often outside the classroom.

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?

  1. Let s be the snack cost.
  2. Write 9 + s = 15.
  3. Subtract 9 from both sides: s = 6.
  4. Connect the calculation back to Word Problems and Modeling so the method, not just the arithmetic, is clear.

Answer: 6 dollars

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. A notebook costs 4 dollars and a pen costs 2 dollars. What is the total?

Show solution
  1. Add the two costs.
  2. 4 + 2 = 6.

Answer: 6

2. Mia has 18 cards and gives away 7. How many remain?

Show solution
  1. Giving away means subtract.
  2. 18 - 7 = 11.

Answer: 11

3. The phrase '5 more than x' means...

Choices: x + 5 · x - 5 · 5x · x/5

Show solution
  1. More than means addition.
  2. 5 more than x is x + 5.

Answer: x + 5

4. A class has 6 tables with 4 students at each table. How many students are there?

Show solution
  1. Each table has 4 students.
  2. 6 x 4 = 24.

Answer: 24

5. A bill of 45 dollars is split equally among 5 people. How much does each person pay?

Show solution
  1. Split equally means divide.
  2. 45 divided by 5 equals 9.

Answer: 9

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