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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.

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.

Answer: 6 dollars

Practice problems

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

Show solution
  1. 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?
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Add the two costs.
  4. 4 + 2 = 6.
  5. 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
  1. Warm-up: First identify exactly what the question is asking: Mia has 18 cards and gives away 7. How many remain?
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Giving away means subtract.
  4. 18 - 7 = 11.
  5. 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
  1. Warm-up: First identify exactly what the question is asking: The phrase '5 more than x' means...
  2. For data questions, identify what each statistic measures before calculating so the result matches the question.
  3. More than means addition.
  4. 5 more than x is x + 5.
  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
  1. 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?
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Each table has 4 students.
  4. 6 x 4 = 24.
  5. 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
  1. 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?
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Split equally means divide.
  4. 45 divided by 5 equals 9.
  5. 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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