Solving Percentage Word Problems
Solving Percent Word Problems: what to notice and how to work it
What to notice first
Common student mistake
Key formulas and cues
A reliable path
- Label unitsWrite what each number measures.
- Build matching ratiosPlace the same units in the same positions.
- Solve and interpretUse cross-products or a unit rate, then attach the correct unit.
Worked examples
Find a unit rate
- Divide total cost by number of notebooks.
- 12 divided by 3 is 4.
- Attach the unit.
Solve a proportion
- The second denominator is 3 times 8.
- Multiply 5 by 3.
- Keep the ratios matched.
Try one before moving on
Solving Percent Word Problems: pop-up practice
Percentage word problems come in three types: find the part, find the percent, or find the whole. Once you recognize which type you have, you plug the known values into one formula and solve. This guide covers all three types with clear examples you can apply directly on the GED.
What Are the Three Types of Percentage Word Problems?
Every percentage problem involves three quantities: the Part, the Percent, and the Whole. The relationship is:
\(\color{blue}{\text{ Part } = \text{ Percent } \times \text{ Whole }}\)
Depending on which value is missing, you rearrange:
- Find the Part: \(\color{blue}{\text{ Part } = \text{ Percent }}\) \(\color{blue}{(\text{ decimal }) \times \text{ Whole }}\)
- Find the Percent: \(\color{blue}{\text{ Percent } = \text{ Part }}\) ÷ \(\color{blue}{\text{ Whole } \times 100}\)
- Find the Whole: \(\color{blue}{\text{ Whole } = \text{ Part }}\) ÷ Percent (decimal)
How to Solve Percentage Word Problems
Type 1 — Find the Part
Key phrase: “What is X% of Y?”
Method: Convert X% to decimal, multiply by Y.
Type 2 — Find the Percent
Key phrase: “A is what percent of B?” or “What percent is A of B?”
Method: Divide A by B, then multiply by 100.
Type 3 — Find the Whole
Key phrase: “X% of what number is A?”
Method: Divide A by the decimal form of X%.
Step-by-Step Summary
- Read the problem and identify what is missing (part, percent, or whole).
- Write the formula that solves for the missing value.
- Convert the percent to a decimal (divide by 100).
- Substitute known values and calculate.
- Check your answer makes sense in context.
Watch: Percent Word Problems (Video Lesson)
Math with Mr. J solves all three types of percent word problems with clear worked examples:
Worked Examples
Example 1 (Find the Part): A store is having a 15% sale. If a coat originally costs $160, how much is the discount?
Discount = \(\color{blue}{0.15 \times 160 = $24}\).
Answer: $24 discount
Example 2 (Find the Percent): 18 students out of 72 scored 90 or above. What percent of students scored 90 or above?
Percent = \(\color{blue}{18 &\text{ div }; 72 \times 100 = 0.25 \times 100 = 25\%}\).
Answer: 25%
Example 3 (Find the Whole): 35% of a number is 70. What is the number?
Whole = \(\color{blue}{70 &\text{ div }; 0.35 = 200}\).
Answer: 200
Example 4 (Percent increase): A price increased from $150 to $180. What is the percent increase?
Increase = \(\color{blue}{180 – 150 = 30}\). Percent increase = \(\color{blue}{30 &\text{ div }; 150 \times 100 = 20\%}\).
Answer: 20% increase
More Practice: Solving Percent Problems Without a Calculator
Math with Mr. J shows how to solve percent problems step by step without a calculator:
Exercises
- What is 45% of 180?
- 12 out of 48 students are absent. What percent are absent?
- 80% of a number is 56. What is the number?
- A salary increased from $40,000 to $46,000. What is the percent increase?
- A school raised 60% of its $25,000 fundraising goal. How much has been raised?
- 15% of what amount is $36?
Answers
- \(\color{blue}{81}\)
- \(\color{blue}{25\%}\)
- \(\color{blue}{70}\)
- \(\color{blue}{15\%}\)
- \(\color{blue}{$15,000}\)
- \(\color{blue}{$240}\)
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Frequently Asked Questions
How do I recognize which type of percentage problem I have?
If the question says “what is X% of Y,” find the part. If it asks “what percent is A of B,” find the percent. If it says “X% of what is A,” find the whole.
What is the percent equation?
The percent equation is \(\color{blue}{\text{ Part } = \text{ Percent } \times \text{ Whole }}\). Rearranged: \(\color{blue}{\text{ Percent } = \text{ Part }}\) ÷ Whole; \(\color{blue}{\text{ Whole } = \text{ Part }}\) ÷ Percent. Always use the decimal form of the percent.
How do I calculate percent increase or decrease?
Percent \(\color{blue}{\text{ change } = (|\text{ new } – \text{ old }| &\text{ div }; \text{ old }) \times 100}\). Use the original value as the denominator. A positive result is an increase; a negative result is a decrease.
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