Lesson 88: Multi-Step Equation Word Problems

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• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

This lesson teaches students how to solve multi-step equation word problems by carefully translating words into algebraic equations and solving step by step. Students will apply operations to isolate variables and check solutions within the context of the problem.

Learning Objectives

• Identify key information in a word problem to write an algebraic equation.
• Solve multi-step equations involving addition, subtraction, multiplication, and division.
• Check solutions by substituting back into the original word problem context.

Topics Covered

• Translating word problems into equations
• Solving multi-step linear equations
• Validating solutions in context

Key Terms

• Variable: A symbol, often x, representing an unknown number.
• Equation: A mathematical statement that two expressions are equal.
• Multi-Step Equation: An equation requiring more than one operation to solve for the variable.

Lesson Examples

Example 1: Finding the cost of a book

1. Read: A book costs $5 more than twice the price of a notebook. If the book costs $25, find the price of the notebook.
2. Translate: Let x = price of the notebook. Equation: 2x + 5 = 25
3. Solve: Subtract 5: 2x = 20, Divide by 2: x = 10. The notebook costs $10.

Example 2: Calculating age

1. Read: Sarah is 3 years older than twice Mike's age. If Sarah is 17, find Mike's age.
2. Translate: Let x = Mike's age. Equation: 2x + 3 = 17
3. Solve: Subtract 3: 2x = 14, Divide by 2: x = 7. Mike is 7 years old.

Practice Problems

1. A shirt costs $8 more than three times the price of a hat. If the shirt costs $32, find the hat's price.
2. Tom has $50. He spends $5 plus twice the amount on a game. How much does he spend on the game?
3. Linda is 4 years younger than half her brother's age. If Linda is 10, how old is her brother?
4. The sum of a number and 7 equals 20. Find the number.

Tips & Common Mistakes

• Carefully identify keywords like “more than” or “less than” when writing equations.
• Perform operations in correct order; check each step for errors.
• Always substitute your solution back into the word problem to verify accuracy.

Summary

Solving multi-step equation word problems requires translating real-life scenarios into algebraic equations, solving step by step, and verifying the solution. This approach strengthens both problem-solving and algebraic reasoning skills.

Challenge Problems

1. A movie ticket costs $3 more than twice the price of popcorn. If the total cost is $15, find the price of the popcorn.
2. Jenny has twice as many pencils as Mark. Together they have 18 pencils. How many pencils does each person have?
3. The sum of three consecutive integers is 45. Find the integers.