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

15 Word Problems

Collect 15 Points

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.

Step-by-Step Solution

**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.