Solving Multi-Step Equations Worksheet

Solving Multi-Step Equations Worksheet


Grade Levels
7th to 9th Grade

Focused Skills
Multi-Step Equation Solving, Algebraic Thinking, Word Problem Interpretation, Arithmetic and Basic Operations, Logical Reasoning, Understanding Proportions and Relationships, Problem-Solving Strategy Development, Critical Thinking

File Format
Printable PDF and Online Math Quiz

Solving Multi-Step Equations Word Problems – Try Interactive Worksheet

15 Word Problems
Collect 15 Points

Alice has 3 more than twice the number of apples that Ben has. If Ben has 4 apples, how many does Alice have?

Sam's garden has 8 rose bushes. Each bush has 6 roses. How many roses are in the garden?

If there are 5 rows of chairs with 6 chairs in each row, how many chairs are there in total?

Tom bought 5 notebooks. Each notebook costs $3. How much did Tom spend on notebooks?

Mark has 2 times the number of pencils as John. If John has 5 pencils, how many pencils does Mark have?

A rectangle has a length of 6 cm and a width that is 2 cm less than the length. What is the width?

Anna has $40. She spends $12 on lunch and $15 on a book. How much money does she have left?

A book has 120 pages. If you read 30 pages a day, how many days will it take to finish the book?

David buys 4 pencils at $2 each and a notebook for $6. How much does he spend in total?

A bag contains 20 marbles. If 5 are red, 8 are blue, and the rest are green, how many green marbles are there?

If there are 12 cookies and you divide them equally among 4 friends, how many cookies does each friend get?

Mike is 3 years younger than twice Jane's age. If Jane is 5, how old is Mike?

There are 4 times as many dogs as cats in a shelter. If there are 3 cats, how many dogs are there?

A movie ticket costs $12. If Kevin buys 3 tickets, how much will he spend?

If the perimeter of a square is 36 cm, what is the length of one side?


 

About Solving Multi-Step Equations Worksheet

This multi-step equations worksheet is designed for 7th to 9th-grade students. It offers a challenging and engaging set of 15-word problems. These problems require students to apply their knowledge of algebra to solve real-world situations, transforming complex scenarios into algebraic expressions and equations. By working through this worksheet, students will enhance their problem-solving abilities and deepen their understanding of multi-step equations.

The worksheet focuses on key skills such as multi-step equation solving, where students learn how to handle multiple operations in a single problem, improving their ability to simplify and solve equations effectively. It also encourages algebraic thinking, helping students understand how to represent everyday situations mathematically. Furthermore, word problems require logical reasoning and word problem interpretation, enabling students to read and comprehend the questions while identifying the important details necessary to find solutions.

This worksheet emphasizes arithmetic and basic operations in addition to algebraic skills, as students need to apply addition, subtraction, multiplication, and division in various contexts. They will also develop a solid grasp of proportions and relationships frequently used in the problems. This helps students understand how different quantities relate to each other, especially in real-life situations.

The benefits of this worksheet for 7th to 9th graders are substantial. It serves as a robust tool for reinforcing critical mathematical concepts that form the foundation for higher-level math courses. By encouraging students to practice problem-solving strategies, it instills a step-by-step and logical approach to equations. Moreover, the worksheet fosters critical thinking, empowering students to analyze and evaluate their work for accurate results.

This worksheet, available for download in PDF format, offers students the flexibility to practice offline. Additionally, it is accessible as an interactive quiz online, providing immediate feedback and enhancing the learning experience.

How to Solving Multi-Step Equations Word Problem
Step-by-Step Solution


“John is twice as old as his sister. In 5 years, their total age will be 35. How old is John now?”


Understand the Problem:

  • Let’s assign a variable to the unknown quantity. In this case, John’s current age is unknown.
  • We are told that John is twice as old as his sister.
  • In 5 years, the total of their ages will be 35.

Define the Variables:

  • Let’s define the sister’s current age as x.
  • Since John is twice as old, we can express John’s current age as 2x.

Set Up the Equation:

  • In 5 years, John’s age will be 2x + 5.
  • Similarly, in 5 years, his sister’s age will be x + 5.
  • We know that in 5 years, the total of their ages will be 35, so the equation becomes: (2x+5)+(x+5)=35

Solve the Equation:

  • Combine like terms:
    2x+5+X+5=35
    3x+10=35
  • Subtract 10 from both sides to isolate the term with the variable: 3x=25
  • Divide both sides by 3 to solve for x: x=3/25​≈8.33

Interpret the Solution:

  • John’s sister is approximately 8.33 years old now.
  • Since John is twice as old as his sister, John’s current age is:
    2x=2×8.33=16.67≈17 years old.

Thus, John is approximately 17 years old now.