Algebra Lessons

Percent Word Problems: How to Solve Them, With Practice

One equation solves most percent word problems. Learn to set it up for discounts, tax, percent change, and interest, then practice.

Professor Chacha October 9, 2026 5 min read 5 views
Woman in glasses counting cash at a table covered with receipts and a calculator

Almost every percent word problem is the same equation in disguise:

\[\text{part} = \text{percent} \times \text{whole}\]

The problem gives you two of the three and asks for the third. Once you can tell which number is the part and which is the whole, the arithmetic is the easy part. This lesson shows how to spot them, how to handle percent change, discounts, tax, and interest, and the traps that placement tests are built around.

The three kinds of percent questions

What you're asked Example How to solve it
Find the part What is 15% of $80? \(0.15 \times 80 = 12\)
Find the percent 9 is what percent of 36? \(\tfrac{9}{36} = 0.25 = 25\%\)
Find the whole 18 is 40% of what number? \(\tfrac{18}{0.40} = 45\)

A reliable way to sort the numbers: the whole usually comes right after the word "of." The part is the piece of it the problem talks about: the tip, the discount, the students who passed.

Percent change: increase and decrease

\[\text{percent change} = \frac{\text{new} - \text{original}}{\text{original}}\]

A rent that goes from $120 to $150 a week increased by \(\tfrac{150 - 120}{120} = \tfrac{30}{120} = 25\%\). If the answer is negative, it is a decrease.

The denominator is always the original amount. Dividing by the new amount is the single most common mistake in this whole topic.

Discounts, tax, and tips in one step

Instead of finding the percent and then adding or subtracting, multiply by what is left:

  • 20% off means you pay 80%: multiply by 0.80.
  • 8% tax means you pay 108%: multiply by 1.08.
  • A 15% tip means the total is 115% of the bill: multiply by 1.15.

This shortcut is also how you work backward. If a jacket costs $36 after 20% off, then \(0.80 \times p = 36\), so the original price was \(\tfrac{36}{0.80} = \$45\). Adding 20% to $36 gives $43.20, which is wrong, because the 20% was taken from the original price, not from $36.

Two percents in a row

When one percent is applied after another, multiply both factors. They don't add. A $2,000 price that goes up 10% and then down 10% ends at

\[2000 \times 1.10 \times 0.90 = 1980\]

not back at $2,000. The 10% decrease is taken from a bigger number, so it removes more than the increase added.

Simple interest

Simple interest is a percent of the starting amount, earned once per year:

\[I = Prt\]

\(P\) is the principal (the starting amount), \(r\) is the yearly rate as a decimal, and \(t\) is the time in years. The GED formula sheet gives you this formula, but you still have to turn 4% into 0.04.

Practice: percent word problems

These eight questions cover every type above, in the style of the ACCUPLACER, TSIA2, and GED math tests.

1.The bill at a restaurant is $42. You leave an 18% tip. How much is the tip?

  1. A$49.56
  2. B$7.56
  3. C$0.76
  4. D$75.60
Show solution \[\text{tip} = 0.18 \times 42 = 7.56\]

Common trap: Answering $49.56, which is the bill plus the tip. Read the last line of the question: it asks for the tip only.

Answer: B ($7.56)

2.In a class, 27 out of 45 students passed a quiz. What percent passed?

  1. A45%
  2. B27%
  3. C60%
  4. D40%
Show solution \[\tfrac{27}{45} = 0.60 = 60\%\]

Common trap: Answering 40%, which is the percent who did not pass. The part (27) goes on top and the whole class (45) goes on the bottom.

Answer: C (60%)

3.30% of a number is 24. What is the number?

  1. A80
  2. B7.2
  3. C54
  4. D30
Show solution

Here the whole is unknown. Write the equation and divide.

\[\begin{gathered}0.30 \times n = 24 \\ \Rightarrow\; n = \tfrac{24}{0.30} = 80\end{gathered}\]

Check: 30% of 80 is 24.

Common trap: Finding 30% of 24 instead, which gives 7.2. The words "of a number" tell you the number is the whole.

Answer: A (80)

4.The price of a TV drops from $250 to $200. By what percent did the price decrease?

  1. A25%
  2. B50%
  3. C80%
  4. D20%
Show solution \[\tfrac{250 - 200}{250} = \tfrac{50}{250} = 0.20 = 20\%\]

Common trap: Dividing by the new price: \(\tfrac{50}{200} = 25\%\). Percent change always compares to the original amount.

Answer: D (20%)

5.After a 15% discount, a shirt costs $34. What was the original price?

  1. A$39.10
  2. B$40.00
  3. C$28.90
  4. D$49.00
Show solution

After 15% off, you pay 85% of the original price.

\[\begin{gathered}0.85 \times p = 34 \\ \Rightarrow\; p = \tfrac{34}{0.85} = 40\end{gathered}\]

Common trap: Adding 15% to the sale price: \(34 \times 1.15 = 39.10\). The 15% was taken from the original price, not from $34, so you have to divide.

Answer: B ($40.00)

6.A town of 5,000 people grows by 10% one year and by another 10% the next year. What is the population after two years?

  1. A6,000
  2. B5,500
  3. C6,050
  4. D6,100
Show solution \[\begin{gathered}5{,}000 \times 1.10 = 5{,}500 \\ 5{,}500 \times 1.10 = 6{,}050\end{gathered}\]

Common trap: Adding the percents to get 20% and answering 6,000. The second 10% is taken from 5,500, so it adds 550 people, not 500.

Answer: C (6,050)

7.You deposit $1,200 in an account that pays 4% simple interest per year. How much interest do you earn in 3 years?

  1. A$144
  2. B$48
  3. C$1,344
  4. D$1,440
Show solution

Simple interest uses \(I = Prt\): principal times rate times time.

\[I = 1200 \times 0.04 \times 3 = 144\]

Common trap: Stopping after one year ($48), or answering $1,344, which is the total balance. The question asks for the interest only.

Answer: A ($144)

8.A pair of headphones costs $64 before tax. The sales tax is 7.5%. What is the total cost?

  1. A$4.80
  2. B$59.20
  3. C$6.88
  4. D$68.80
Show solution \[64 \times 1.075 = 68.80\]

Or in two steps: the tax is \(64 \times 0.075 = 4.80\), and \(64 + 4.80 = 68.80\).

Common trap: Writing 7.5% as 0.75 instead of 0.075. Move the decimal point exactly two places: \(7.5\% = 0.075\).

Answer: D ($68.80)

Teacher's note: The trick I teach for setting up any percent problem is to translate it word for word: "of" becomes times, "is" becomes equals, and "what" becomes the unknown. "30% of what number is 24" turns into \(0.30 \times n = 24\) without any thinking about which formula to use. Write the sentence as an equation first, then solve.

Tags: Algebra Interest Percents Word problems
Professor Chacha
Professor Chacha Math teacher and educational psychologist

Math teacher and educational psychologist with more than 20 years of classroom experience. He writes every practice question on this site from scratch and solves it step by step, the way he explains it to his own students.

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