ACT Math Percents: 12 Practice Problems with Step-by-Step Explanations
Percents are one of the most versatile topics on the ACT Math section, appearing not just as standalone questions like "what is 80% of 50?" but woven into word problems about investments, mixtures, geometry, and multi-step real-world scenarios. On a typical ACT, you'll see anywhere from three to six questions that require percent reasoning, and the topic scales in difficulty faster than almost any other chapter — the same underlying skill, converting between percents, decimals, and fractions, gets tested in problems ranging from a single calculation to five-step scenarios with multiple percentages layered on top of each other.
The core formulas are straightforward: "percent of" means multiply by the decimal form of the percent, and "X is what percent of Y" means divide X by Y. The real difficulty comes from multi-step problems where percentages apply to different bases at each step. For example, when a problem describes 26% of 48% of a total, you cannot add those percentages together — you have to multiply them as successive fractions of a shrinking group. Similarly, in percent-change problems, like reselling an item at a markup, each percentage applies to the result of the previous step, not to the original amount.
Common traps include mixing up "percent of the original" with "percent of the new value," forgetting to convert a percent to a decimal before multiplying, and adding percentages that should be multiplied instead. Work through the 12 problems below, then click to reveal each explanation to check your reasoning.
On this page:
- Problem 1 — Percent of a number
- Problem 2 — Percent correct
- Problem 3 — Percent of a total
- Problem 4 — Finding the original number
- Problem 5 — Equivalent percent expressions
- Problem 6 — Best possible percent
- Problem 7 — Multi-step percent allocation
- Problem 8 — Percent to find a total, then a difference
- Problem 9 — Successive percent change
- Problem 10 — Nested percentages
- Problem 11 — Percent applied to volume
- Problem 12 — Mixture problem
Practice Problems
What is 80% of 50?
- A) 10
- B) 20
- C) 40
- D) 42
Convert 80% to a decimal (0.80) and multiply: 0.80 × 50 = 40.
On his English test, Justin missed 8 of the 50 questions. What percentage did Justin answer correctly?
- A) 16%
- B) 40%
- C) 75%
- D) 84%
If Justin missed 8 of 50 questions, he answered 50 − 8 = 42 correctly. As a percentage: 42/50 = 0.84 = 84%.
Answer choice A (16%) is the percent he got wrong, not the percent he got right — a common trap for students who solve for the wrong quantity.
Jim is a farmer. Last year he planted 280 acres of corn and 420 acres of soybeans. What percent of the acres Jim planted was corn?
- A) 28%
- B) 40%
- C) 66%
- D) 75%
The total acres planted is 280 + 420 = 700. The percent that was corn is 280/700 = 0.40 = 40%.
Answer choice D (75%) is a trap for students who divide corn acres by soybean acres instead of by the total.
48 is 150% of what number?
- A) 24
- B) 30
- C) 32
- D) 40
Set up the equation 48 = 1.50 × n, where n is the unknown number. Solving: n = 48 / 1.50 = 32.
If 8% of x is the same as 10% of 120, what is the value of x?
- A) 9.6
- B) 15
- C) 116
- D) 150
10% of 120 is 0.10 × 120 = 12. Set that equal to 8% of x: 0.08x = 12. Solving for x: x = 12 / 0.08 = 150.
As Max is grading his math homework, he has answered 4 of the first 35 questions incorrectly. If the homework has a total of 40 questions, what is the highest possible percent correct that Max can earn on his homework?
- A) 83%
- B) 89%
- C) 90%
- D) 93%
Of the first 35 questions, Max got 35 − 4 = 31 correct. There are 40 − 35 = 5 questions remaining, and for the highest possible score, assume he answers all 5 correctly. That gives 31 + 5 = 36 correct out of 40 total.
36/40 = 0.90 = 90%.
Pamela has $2,000. She decides to invest 30% in stocks, (3x − 11)% in bonds, x% in mutual funds, and to keep the rest in cash. She invests twice as much in mutual funds as she keeps in cash. How many dollars does Pamela keep in cash?
- A) 360
- B) 270
- C) 180
- D) 135
Let the cash percentage be c. Since Pamela invests twice as much in mutual funds as she keeps in cash, and both are percentages of the same total, the mutual fund percentage x is twice the cash percentage, so c = x/2.
All the percentages must add to 100: 30 + (3x − 11) + x + x/2 = 100. Combine like terms: 19 + 4.5x = 100, so 4.5x = 81 and x = 18.
The cash percentage is x/2 = 9%. In dollars, that's 9% of $2,000 = $180.
The groups of students who are graduating with honors from the university have a variety of different majors. 40% are science majors, 15% are history majors, 25% are humanities majors, and the remaining 88 students are all business majors. Of the students graduating with honors, how many more science majors were there than history majors?
- A) 66
- B) 110
- C) 132
- D) 176
Science, history, and humanities majors account for 40% + 15% + 25% = 80% of the class, so business majors make up the remaining 20%. Since 88 students represent that 20%, the total class size is 88 / 0.20 = 440 students.
Science majors: 0.40 × 440 = 176. History majors: 0.15 × 440 = 66. The difference is 176 − 66 = 110.
Rebecca sells her pickup truck to Jeremy for 76% of the original price. Jeremy does some work on the car and then sells it for 110% of the price that he purchased the car for. Which of the following is closest to percent of the original price that Jeremy sold the car for?
- A) 70
- B) 84
- C) 86
- D) 93
Jeremy purchased the truck for 76% of the original price. He then sold it for 110% of what he paid, which means the two percentages multiply rather than add: 0.76 × 1.10 = 0.836, or 83.6% of the original price.
83.6% rounds to approximately 84%, which is the closest answer choice. This is a classic successive-percentage setup — treating it as 76% + 10% = 86% (choice C) is the trap answer.
48% of the gifts in a donation basket are balls. Of those 48%, 26% are blue. Of the blue balls, 36% are basketballs. Which of the following is closest to the percentage of items in the basket that are NOT blue basketballs?
- A) 0.044%
- B) 4.49%
- C) 87.52%
- D) 95.51%
Each percentage applies to a shrinking group, so multiply them together rather than adding: 0.48 × 0.26 × 0.36 = 0.044928, or about 4.49% of all items are blue basketballs.
The question asks for items that are NOT blue basketballs, so subtract from 100%: 100% − 4.49% = 95.51%.
Big Storage is offering a new storage shed. The original storage shed was 6 feet wide, 10 feet long, and 8 feet tall. The new storage shed's dimensions will be 80% of the original width, 75% of the original length, and 90% of the original height. To the nearest 1%, what percent will the volume of the new storage shed be when compared to the volume of the original storage shed?
- A) 54
- B) 66
- C) 78
- D) 81
Volume is width × length × height, so scaling each dimension by a percentage scales the volume by the product of those percentages: 0.80 × 0.75 × 0.90 = 0.54, or 54%.
The actual dimensions (6, 10, and 8 feet) aren't needed — only the scale factors matter, since volume scales multiplicatively with each dimension.
How many liters of a 40% saline solution must be added to 8 liters of a 10% saline solution to obtain a 30% saline solution?
- A) 12
- B) 16
- C) 24
- D) 32
Let x be the liters of 40% solution added. The total amount of pure saline before and after mixing must be equal: 0.10(8) + 0.40(x) = 0.30(8 + x).
Simplify: 0.8 + 0.4x = 2.4 + 0.3x. Subtract 0.3x from both sides and subtract 0.8 from both sides: 0.1x = 1.6, so x = 16.
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