Solving Percentage Word Problems

How to solving percentage word problems, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

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Solving Percent Word Problems: what to notice and how to work it

Proportional skill

Ratio and proportion problems compare quantities. The key is keeping units aligned so the same kind of quantity sits across from the same kind of quantity.

What to notice first

Translate the story into variables before solving. Units, totals, and comparisons tell you what each expression should represent.

Common student mistake

Do not solve before defining variables. A clear variable definition keeps the equation tied to the story.

Key formulas and cues

$\frac{a}{b}=\frac{c}{d}\Rightarrow ad=bc$

$\text{unit rate}=\frac{\text{amount}}{\text{1 unit}}$

$\text{percent}=\frac{\text{part}}{\text{whole}}\cdot100\%$

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

Example: 3 notebooks cost $12

Divide total cost by number of notebooks.
12 divided by 3 is 4.
Attach the unit.

Answer: $4 per notebook

Solve a proportion

Example: $\frac{5}{8}=\frac{x}{24}$

The second denominator is 3 times 8.
Multiply 5 by 3.
Keep the ratios matched.

Answer: $x=15$

Open pop-up practice

Try one before moving on

Try: 5 tickets cost $40. What is the cost per ticket?

Answer: $8 per ticket.

Next step: do the matching worksheet or quiz while the method is still fresh, then come back and explain the first step in your own words.

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 you solve percentage word problems?

Decide which piece is missing: the part, the whole or the percent. Then use part = percent × whole, writing the percent as a decimal. If 15% of 60 students walk to school, 0.15 × 60 = 9 students walk. If the whole is missing, divide instead: 9 is 15% of 9 ÷ 0.15 = 60. Finish by checking that the answer makes sense in the story.

How do you solve percentage word problems easily?

Build from benchmark percents. To find 10% of a number, move the decimal point one place left; 1% is two places left. For 35% of 80: 10% is 8, so 30% is 24, and 5% is half of 10%, which is 4. Add them to get 28. This mental-math method is fast and also helps you spot a calculator entry mistake.

How do you solve percent change word problems?

Use percent change = (new − original) ÷ original × 100%. If a price rises from $40 to $50, the change is 10, and 10 ÷ 40 = 0.25, a 25% increase. If it falls from $50 to $40, divide by the original 50 instead: 10 ÷ 50 = 0.20, a 20% decrease. Always divide by the starting value, not the new one.

How do you solve percent proportion word problems?

Set up part/whole = percent/100 and cross-multiply. For 18 is what percent of 72, write 18/72 = p/100. Cross-multiplying gives 72p = 1,800, so p = 25, meaning 18 is 25% of 72. The same setup works when the part or the whole is unknown; just place the variable in the right spot.

What is an example of solving a percentage word problem?

A $64 jacket is on sale for 25% off. What is the sale price? The discount is 0.25 × 64 = $16, so the sale price is 64 − 16 = $48. A quicker route is to multiply by the percent you actually pay: 100% − 25% = 75%, and 0.75 × 64 = $48. Sales tax works the same way, except you add it on.

How do you solve word problems involving percentage, rate and base?

The base is the whole amount, the rate is the percent, and the percentage is the part, related by percentage = rate × base. To find the base, divide: if 12 is 30% of a number, base = 12 ÷ 0.30 = 40. To find the rate, divide the percentage by the base: 12 ÷ 40 = 0.30, or 30%.

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Solving Percentage Word Problems