ACT Word Problems Practice Questions with Answers

Mastering ACT word problems is essential for achieving a high score on the math section, as approximately 30% to 40% of the questions are presented in a narrative format. These problems require students to translate written descriptions into mathematical equations and solve for unknown variables. By developing a systematic approach to identifying key information and choosing the right operations, students can navigate even the most complex scenarios efficiently. This guide provides a comprehensive overview of ACT word problems, offering strategies and practice to build your confidence.

Concept Explanation

ACT word problems are mathematical questions presented in a real-world context that require you to interpret text, identify relevant data, and apply algebraic or geometric concepts to find a solution. Success on these problems depends on your ability to "translate" English into Math. For instance, the word "is" typically represents an equals sign $=$, while "of" often indicates multiplication $\times$. Most problems fall into specific categories such as rates, percentages, ratios, averages, or systems of linear equations. To excel in ACT Prep, you must learn to ignore "distractor" information and focus solely on the numbers and relationships that lead to the final answer. Using tools like an AI Question Generator can help you practice these translations across different difficulty levels.

When approaching these questions, follow these four steps:

1. Identify the Goal: Read the last sentence first to understand exactly what the question is asking for.
2. Extract the Data: List the known values and define your variables (e.g., let $x$ be the number of tickets).
3. Set Up the Equation: Convert the relationships described in the text into a mathematical expression.
4. Solve and Verify: Perform the calculation and ensure the units of your answer match the question's requirements.

Solved Examples

Reviewing worked examples is one of the best ways to understand the logic behind mathematical modeling in word problems.

1. Example 1 (Basic Algebra): A local theater sells student tickets for $8 and adult tickets for $12. If a group of 10 people paid a total of $104, how many student tickets were purchased?
   1. Define variables: Let $s$ be the number of student tickets and $a$ be the number of adult tickets.
   2. Set up equations: $s + a = 10$ and $8s + 12a = 104$.
   3. Solve for $a$: From the first equation, $a = 10 - s$.
   4. Substitute: $8s + 12(10 - s) = 104$.
   5. Simplify: $8s + 120 - 12s = 104 \rightarrow -4s = -16$.
   6. Final Answer: $s = 4$.
2. Example 2 (Percentage): A jacket originally priced at $80 is on sale for 25% off. If an additional 10% discount is applied to the sale price at the register, what is the final cost?
   1. Calculate the first discount: $25\% \text{ of } 80 = 0.25 \times 80 = 20$. Sale price = $80 - 20 = 60$.
   2. Calculate the second discount: $10\% \text{ of } 60 = 0.10 \times 60 = 6$.
   3. Final price: $60 - 6 = 54$.
   4. Final Answer: $54.
3. Example 3 (Rate/Time): Sarah can paint a room in 4 hours, and Mark can paint the same room in 6 hours. How long will it take them to paint the room together?
   1. Determine hourly rates: Sarah paints $\frac{1}{4}$ of the room per hour; Mark paints $\frac{1}{6}$ of the room per hour.
   2. Combine rates: $\frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}$.
   3. Solve for time ($t$): $\frac{5}{12} \times t = 1 \text{ (one full room)}$.
   4. Final Answer: $t = \frac{12}{5} = 2.4$ hours.

Practice Questions

1. A rectangular garden has a perimeter of 48 feet. If the length is 4 feet longer than the width, what is the area of the garden in square feet?
2. A car travels 180 miles on 6 gallons of gasoline. At this same rate, how many gallons of gasoline will the car need to travel 450 miles?
3. The sum of three consecutive integers is 72. What is the value of the largest integer?

4. A jar contains 12 red marbles, 8 blue marbles, and 10 green marbles. If one marble is drawn at random, what is the probability that it is NOT blue?
5. A plumber charges a flat fee of $50 plus $35 per hour of work. If a customer's total bill was $190, how many hours did the plumber work?
6. In a class of 30 students, the ratio of boys to girls is 2:3. How many girls are in the class?
7. If $3x + 5 = 2x - 7$, what is the value of $x^2$?
8. A laptop's price is increased by 20% and then decreased by 20%. If the original price was $1,000, what is the final price?
9. A cylindrical water tank has a radius of 3 feet and a height of 10 feet. What is the volume of the tank in cubic feet? (Use $\pi \approx 3.14$)
10. The average of five numbers is 18. If a sixth number, 30, is added to the set, what is the new average?

Answers & Explanations

1. Answer: 140. Let width be $w$ and length be $w + 4$. Perimeter $P = 2(l + w)$, so $48 = 2(w + 4 + w)$. This simplifies to $48 = 2(2w + 4) \rightarrow 48 = 4w + 8$. Subtract 8: $40 = 4w$, so $w = 10$. Length $l = 14$. Area = $10 \times 14 = 140$.
2. Answer: 15. Establish a proportion: $\frac{180 \text{ miles}}{6 \text{ gallons}} = \frac{450 \text{ miles}}{x \text{ gallons}}$. Cross-multiply: $180x = 2700$. Divide by 180: $x = 15$.
3. Answer: 25. Let the integers be $n, n+1, n+2$. Their sum is $3n + 3 = 72$. Subtract 3: $3n = 69$. Divide by 3: $n = 23$. The largest integer is $n+2 = 25$.
4. Answer: 11/15 (or approx 0.73). Total marbles = $12 + 8 + 10 = 30$. Marbles that are not blue = $12 + 10 = 22$. Probability = $\frac{22}{30}$, which reduces to $\frac{11}{15}$.
5. Answer: 4. Equation: $50 + 35h = 190$. Subtract 50: $35h = 140$. Divide by 35: $h = 4$.
6. Answer: 18. The ratio 2:3 means there are 5 parts total ($2+3=5$). Each part is $30 / 5 = 6$. Girls represent 3 parts: $3 \times 6 = 18$.
7. Answer: 144. Solve for $x$: $3x - 2x = -7 - 5 \rightarrow x = -12$. Then $x^2 = (-12)^2 = 144$.
8. Answer: $960. Increase: $1000 \times 1.20 = 1200$. Decrease: $1200 \times 0.80 = 960$.
9. Answer: 282.6. Volume $V = \pi r^2 h$. $V = 3.14 \times (3)^2 \times 10 = 3.14 \times 9 \times 10 = 282.6$.
10. Answer: 20. Sum of first five numbers = $18 \times 5 = 90$. New sum = $90 + 30 = 120$. New average = $120 / 6 = 20$.

1. A shirt costs $20. If the price is increased by 10%, what is the new price?

• A$21
• B$22
• C$23
• D$24

Frequently Asked Questions

What is the most common type of ACT word problem?

Algebraic translation problems are the most frequent, where you must convert a real-world scenario into a linear equation or inequality. These often involve calculating total costs, finding unknown quantities in a group, or solving for a specific variable based on given constraints.

How can I improve my speed on word problems?

Speed improves by practicing active reading—underlining the specific question being asked and circling relevant numbers immediately. Using a AI Exam Simulator can help you get used to the time pressure and identify which problem types you should skip and return to later.

Are calculators allowed for ACT word problems?

Yes, calculators are permitted on the entire ACT math section, provided they are not on the prohibited list. While a calculator helps with arithmetic, the primary challenge of word problems is the setup of the equation, which the calculator cannot do for you.

Do ACT word problems include geometry?

Yes, many geometry questions are phrased as word problems, such as finding the amount of fencing needed for a yard or the volume of water in a pool. You should be familiar with formulas for area, perimeter, and volume as defined by the ACT official standards.

What is the "Backsolving" method?

Backsolving involves taking the provided multiple-choice answer options and plugging them into the word problem to see which one works. This is a highly effective strategy for complex algebra word problems when you are struggling to set up the correct equation manually.

How many word problems are on the ACT?

While the exact number varies by test version, typically 20 to 25 out of the 60 math questions are presented as word problems. These range from simple one-step calculations to multi-step problems found toward the end of the exam.