ACT Percentage Practice Questions with Answers

Mastering ACT percentage problems is a fundamental step toward achieving a high score on the math section, as these concepts appear frequently in both basic arithmetic and complex data analysis questions. An ACT Percentage problem typically requires you to calculate a part of a whole, determine a percentage increase or decrease, or solve multi-step problems involving taxes, discounts, and interest. Understanding how to translate word problems into algebraic equations is the key to efficiency on test day.

Concept Explanation

An ACT percentage is a way of expressing a number as a fraction of 100, represented by the symbol %. To solve most percentage problems on the exam, you should be comfortable with the "is over of" formula, which states that $\ \frac{\ \text{part}}{\ \text{whole}} = \ \frac{\ \text{percent}}{100}$. This ratio allows you to solve for any missing variable by cross-multiplying. For more comprehensive strategies on standardized testing, you can explore our ACT Prep hub.

When preparing for the math section, it is helpful to categorize percentage questions into three main types:

• Basic Percentages: Finding a specific percent of a number (e.g., "What is 15% of 80?").

• Percentage Change: Calculating the increase or decrease between two values using the formula: $\ \frac{\ \text{New} - \ \text{Old}}{\ \text{Old}} \ \times 100$.

• Successive Percentages: Applying multiple percentage changes in a row, such as a discount followed by a sales tax.

It is also vital to understand the relationship between decimals, fractions, and percentages. For example, 25% is equivalent to 0.25 and $\ \frac{1}{4}$. Many students find it faster to use the AI Question Generator to practice these conversions until they become second nature. High-authority resources like Khan Academy provide excellent visualizations of these ratios.

Solved Examples

Review these step-by-step solutions to understand the logic required for ACT-style percentage questions.

1. Example 1 (Basic Percent): A jacket originally costs $120. It is on sale for 30% off. What is the sale price of the jacket?

   1. Identify the discount amount: $120 \ \times 0.30 = 36$.

   2. Subtract the discount from the original price: $120 - 36 = 84$.

   3. The sale price is $84.

2. Example 2 (Percent Change): The population of a small town increased from 5,000 to 6,200 people. What was the percentage increase?

   1. Find the amount of increase: $6,200 - 5,000 = 1,200$.

   2. Divide the increase by the original population: $\ \frac{1,200}{5,000} = 0.24$.

   3. Convert the decimal to a percentage: $0.24 \ \times 100 = 24\%$.

3. Example 3 (Reverse Percentage): After a 15% tip was added, a restaurant bill totaled $46.00. What was the original cost of the meal before the tip?

   1. Let $x$ be the original cost. The total is $115\%$ of $x$.

   2. Set up the equation: $1.15x = 46$.

   3. Solve for $x$: $x = \ \frac{46}{1.15} = 40$.

   4. The original meal cost $40.00.

Practice Questions

Test your skills with these practice questions ranging from easy to hard difficulty.

1. What is 45% of 240?

2. A laptop is priced at $800. If a 7% sales tax is added, what is the final cost?

3. A student scored an 85% on a test with 60 questions. How many questions did the student answer correctly?

4. A car's value depreciated from $25,000 to $21,000 in one year. What was the percentage decrease?

5. If 12 is 15% of a number $n$, what is the value of $n$?

6. A store offers a "Buy One, Get One 50% Off" deal on shirts that cost $30 each. If a customer buys two shirts, what is the total percentage discount on the entire purchase?

7. In a group of 200 people, 40% are under the age of 18. Of those under 18, 25% are under the age of 5. How many people in the group are under the age of 5?

8. A stock price increased by 20% on Monday and then decreased by 10% on Tuesday. What was the total percentage change from the original price?

9. A rectangle's length is increased by 20% and its width is decreased by 20%. What is the percentage change in the area of the rectangle?

10. A jar contains red, blue, and green marbles. 30% are red and 45% are blue. If there are 50 green marbles, how many total marbles are in the jar?

If you find these calculations challenging, you might also benefit from reviewing related mathematical concepts in our pharmacokinetics calculation or creatinine clearance guides, which use similar ratio-based logic. For a more intensive experience, try the AI Exam Simulator.

Answers & Explanations

1. Answer: 108. Calculation: $240 \ \times 0.45 = 108$.

2. Answer: $856. Calculation: $800 \ \times 0.07 = 56$. Total = $800 + 56 = 856$.

3. Answer: 51. Calculation: $60 \ \times 0.85 = 51$.

4. Answer: 16%. Calculation: $\ \frac{25,000 - 21,000}{25,000} = \ \frac{4,000}{25,000} = 0.16$. $0.16 \ \times 100 = 16\%$.

5. Answer: 80. Calculation: $0.15n = 12$. $n = \ \frac{12}{0.15} = 80$.

6. Answer: 25%. Calculation: Total original price = $30 + 30 = 60$. Sale price = $30 + 15 = 45$. Discount = $60 - 45 = 15$. Percentage discount = $\ \frac{15}{60} = 0.25$ or 25%.

7. Answer: 20. Calculation: Under 18 = $200 \ \times 0.40 = 80$. Under 5 = $80 \ \times 0.25 = 20$.

8. Answer: 8% increase. Calculation: Let original price be 100. After Monday: $100 \ \times 1.20 = 120$. After Tuesday: $120 \ \times 0.90 = 108$. Increase from 100 to 108 is 8%.

9. Answer: 4% decrease. Calculation: Area = $L \ \times W$. New Area = $(1.20L) \ \times (0.80W) = 0.96LW$. 0.96 is a 4% decrease from 1.00.

10. Answer: 200. Calculation: Green percentage = $100\% - (30\% + 45\%) = 25\%$. If 25% of Total = 50, then $0.25T = 50$. $T = \ \frac{50}{0.25} = 200$.

1. If a $50 shirt is marked down by 20%, what is the new price?

• A$30
• B$40
• C$45
• D$10

Frequently Asked Questions

How do I calculate percentage increase on the ACT?

To calculate percentage increase, subtract the original value from the new value, divide that difference by the original value, and multiply the result by 100. This formula ensures you are measuring the growth relative to the starting point.

What is the fastest way to find a percentage on a calculator?

The fastest way is to convert the percentage to a decimal by moving the decimal point two places to the left and multiplying it by the whole number. For example, to find 18% of 50, simply type "0.18 * 50" into your calculator.

Can a percentage be greater than 100?

Yes, a percentage greater than 100 indicates that the part is larger than the original whole, which often occurs in growth or profit scenarios. For instance, 150% of a number is 1.5 times that number.

How do successive discounts work?

Successive discounts are applied one after another to the remaining balance, not the original total. If an item is 20% off and then another 10% off, you multiply the original price by 0.80 and then multiply that new result by 0.90.

What does "percent of" mean in math terms?

In math word problems, the word "of" almost always signifies multiplication. When you see "25% of 80," you should translate it into the mathematical expression $0.25 \ \times 80$.

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