Percent Change Word Problems Made Easy for Students

Mastering Percent Change Word Problems: A Comprehensive Guide for Students

Percent change word problems can be intimidating, especially for students who struggle with math. However, with a clear understanding of the concepts and a step-by-step approach, these problems can become manageable and even enjoyable. In this article, we will break down the key concepts, provide examples, and offer tips to help students master percent change word problems.

Understanding Percent Change

Percent change refers to the difference between two values, expressed as a percentage of the original value. It is a common concept used in various real-life situations, such as calculating discounts, markups, and changes in stock prices.

Key Concepts:

• Original value: The initial value before any change occurs.
• New value: The final value after the change occurs.
• Percent increase: An increase in value, calculated as a percentage of the original value.
• Percent decrease: A decrease in value, calculated as a percentage of the original value.

Types of Percent Change Word Problems

There are several types of percent change word problems, including:

• Simple percent change: A straightforward problem involving a single percent change.
• Multi-step percent change: A problem involving multiple percent changes.
• Percentage of a percentage: A problem involving a percentage of a percentage.

Solving Simple Percent Change Word Problems

To solve simple percent change word problems, follow these steps:

1. Read the problem carefully: Understand the original value, new value, and percent change.
2. Determine the type of percent change: Identify whether it is a percent increase or decrease.
3. Calculate the percent change: Use the formula: percent change = ((new value - original value) / original value) x 100.
4. Solve for the unknown value: Use the calculated percent change to find the unknown value.

Example 1: Simple Percent Increase

A shirt originally costs 20. After a 15% increase, the new price is 23. What is the percent increase?

• Original value: $20
• New value: $23
• Percent change: ((23 - 20) / 20) x 100 = 15%

Example 2: Simple Percent Decrease

A book originally costs 30. After a 10% decrease, the new price is 27. What is the percent decrease?

• Original value: $30
• New value: $27
• Percent change: ((27 - 30) / 30) x 100 = -10%

Solving Multi-Step Percent Change Word Problems

To solve multi-step percent change word problems, follow these steps:

1. Break down the problem: Identify each percent change and the order in which they occur.
2. Calculate each percent change: Use the formula: percent change = ((new value - original value) / original value) x 100.
3. Combine the percent changes: Calculate the overall percent change by multiplying each percent change together.

Example 3: Multi-Step Percent Change

A company increases the price of a product by 10% and then decreases it by 5%. What is the overall percent change?

• Original value: $100
• First percent change: 10% increase = $110
• Second percent change: 5% decrease = 110 x 0.05 = 5.50
• Overall percent change: (110 - 5.50) / $100 = 4.5%

Solving Percentage of a Percentage Word Problems

To solve percentage of a percentage word problems, follow these steps:

1. Identify the percentage of a percentage: Recognize that the problem involves a percentage of a percentage.
2. Calculate the first percentage: Use the formula: percent change = ((new value - original value) / original value) x 100.
3. Calculate the second percentage: Use the formula: percent change = ((new value - original value) / original value) x 100.
4. Combine the percentages: Calculate the overall percent change by multiplying each percent change together.

Example 4: Percentage of a Percentage

A store offers a 20% discount on a product that is already 15% off. What is the overall discount?

• Original value: $100
• First discount: 15% = $15
• Second discount: 20% of 85 = 17
• Overall discount: 15 + 17 = $32

Tips and Tricks

• Read the problem carefully: Understand the original value, new value, and percent change.
• Use a calculator: Simplify calculations by using a calculator.
• Check your units: Ensure that the units of measurement are consistent throughout the problem.
• Practice, practice, practice: The more you practice, the more confident you will become in solving percent change word problems.

💡 Note: Percent change word problems can be challenging, but by breaking them down into smaller steps and practicing regularly, you can become proficient in solving them.

In conclusion, mastering percent change word problems requires a clear understanding of the concepts, a step-by-step approach, and practice. By following the tips and tricks outlined in this article, students can become more confident and proficient in solving these types of problems.

Related Terms:

• Percent of change Worksheet PDF