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ACT Math Help: Word Problems

Review real example questions for Word Problems in ACT Math.

Question 1 / 10

0 of 10 answered

A car rental company charges a flat base fee of $30 plus $0.15 for every mile driven. If a customer's total rental cost (before taxes) is $63, how many miles did the customer drive?

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Question 1

A car rental company charges a flat base fee of $30 plus $0.15 for every mile driven. If a customer's total rental cost (before taxes) is $63, how many miles did the customer drive?

  1. 120
  2. 180
  3. 220 (correct answer)
  4. 310

Explanation: The correct answer is C (220). Set up the equation: base fee + per-mile charge = total cost → 30 + 0.15m = 63 → 0.15m = 33 → m = 33 ÷ 0.15 = 220 miles. A (120) likely results from an arithmetic error when dividing 33 by 0.15, possibly misplacing a decimal. B (180) is another arithmetic error in the division. D (310) could result from failing to subtract the base fee, using the full $63 as the variable amount, then dividing incorrectly. The key step is subtracting the flat fee before dividing by the per-unit rate.

Question 2

A teacher is making identical gift bags with 42 pencils and 63 stickers, no items left over, same number of each item per bag. What is the greatest number of bags she can make?

  1. 3
  2. 7
  3. 14
  4. 21 (correct answer)

Explanation: This is a Greatest Common Factor (GCF) question embedded in a real-world context. Choice D (21) is correct — the GCF determines the maximum number of identical bags with no items left over. Factor both numbers: 42 = 2 × 3 × 7 and 63 = 3² × 7. GCF = 3 × 7 = 21. Check: 42 ÷ 21 = 2 pencils per bag; 63 ÷ 21 = 3 stickers per bag. No remainder either way. Choice A (3) identifies a common factor (3 divides both 42 and 63) but not the greatest one. Choice B (7) identifies another common factor but also not the greatest. Choice C (14) = 42 ÷ 3, which is not a factor of 63 (63 ÷ 14 = 4.5). Pro tip: "Greatest number of identical groups with nothing left over" always means GCF. List prime factors of both numbers and multiply all shared prime factors together. The GCF of 42 and 63 is not their product (2,646) divided by anything — it's the product of their shared factors only.

Question 3

A classroom has 2828 students. The teacher forms groups with 44 students in each group. How many groups can be formed?

  1. 77 groups (correct answer)
  2. 2424 groups
  3. 3232 groups
  4. 112112 groups

Explanation: We need to find how many groups of 4 can be formed from 28 students. This requires division: number of groups = total students ÷ students per group. So we calculate 28 ÷ 4 = 7 groups. Choice D (112) incorrectly multiplies 28 × 4 instead of dividing.

Question 4

A train travels 210 miles in 3.5 hours at a constant speed. What is the train's speed in miles per hour?

  1. 0.0167 miles per hour
  2. 73.5 miles per hour
  3. 60 miles per hour (correct answer)
  4. 735 miles per hour

Explanation: We need to find the train's speed using the formula speed = distance ÷ time. The train travels 210 miles in 3.5 hours, so speed = 210 miles ÷ 3.5 hours = 60 miles per hour. Choice B (73.5 mph) would result from incorrectly adding the distance and time instead of dividing.

Question 5

A chemist has two solutions: Solution A is 2020\\% acid and Solution B is 5050\\% acid.

How many milliliters of Solution A must be mixed with 40 milliliters of Solution B to obtain a mixture that is 3030\\% acid?

  1. 40
  2. 60
  3. 80 (correct answer)
  4. 100

Explanation: This is a mixture problem testing weighted average setup. Choice C (80 mL) is correct — let x = mL of Solution A. Set up the equation: acid contributed by A + acid contributed by B = acid in the final mixture: 0.20x + 0.50(40) = 0.30(x + 40). Simplify: 0.20x + 20 = 0.30x + 12. Solve: 8 = 0.10x → x = 80 mL. Choice A (40 mL) assumes equal volumes of both solutions, which would produce a 35% mixture (the average of 20% and 50%), not 30%. Choice B (60 mL) results from a setup or arithmetic error, possibly not distributing 0.30 across the full total volume on the right side. Choice D (100 mL) results from a sign or distribution error in solving the equation, perhaps writing 0.30(40) instead of 0.30(x + 40) for the right side. Pro tip: The mixture equation template is: %(A) × vol(A) + %(B) × vol(B) = %(mixture) × total volume. Always express the total volume as (vol A + vol B), and use the target percentage on the full mixture — not just one component.

Question 6

A worker earns $15.00 per hour for the first 40 hours worked in a week. For any hours worked over 40, the worker earns $22.50 per hour. If the worker works 46 hours in one week, what is the total amount earned?

  1. $690.00
  2. $735.00 (correct answer)
  3. $750.00
  4. $1{,}035.00

Explanation: This is an arithmetic and rates question testing overtime pay calculations. Choice B ($735.00) is correct — regular pay for the first 40 hours: 40 × $15.00 = $600.00. Overtime hours: 46 − 40 = 6 hours. Overtime pay: 6 × $22.50 = $135.00. Total: $600 + $135 = 735.00.ChoiceA(735.00. Choice A (690.00) applies the regular $15.00 rate to all 46 hours, ignoring the overtime premium entirely: 46 × $15 = 690.ChoiceC(690. Choice C (750.00) results from a small arithmetic error in the overtime calculation — possibly computing 6 × $25 = 150instead.ChoiceD(150 instead. Choice D (1,035.00) applies the overtime rate of $22.50 to all 46 hours, as if the entire shift were overtime: 46 × $22.50 = $1,035. Pro tip: Always split overtime problems into two separate calculations — regular hours at base pay, overtime hours at the elevated rate — then add. Never apply one rate to the full total.

Question 7

Pump A can fill a tank in 4 hours alone. Pump B can fill the same tank in 6 hours alone. How many hours will it take both pumps working together to fill the tank?

  1. 2
  2. 2.4 (correct answer)
  3. 5
  4. 10

Explanation: This is a work rates question testing the combined rate method. Choice B (2.4 hours) is correct — convert each pump's time into a rate (fraction of the tank filled per hour): Pump A fills 1/4 of the tank per hour; Pump B fills 1/6 of the tank per hour. Working together, their rates add: 1/4 + 1/6 = 3/12 + 2/12 = 5/12 of the tank per hour. Time to fill one full tank = 1 ÷ (5/12) = 12/5 = 2.4 hours. Choice A (2.0 hours) comes from averaging the two times and halving: (4 + 6)/2 = 5, then 5/2 = 2.5... or simply assuming two pumps cut the faster pump's time in half: 4/2 = 2. Neither approach is valid — the combined time depends on both rates, not just the faster one. Choice C (5.0 hours) averages the two times directly: (4 + 6)/2 = 5 — a common intuition that produces a result slower than either pump alone, which should immediately signal an error. Choice D (10.0 hours) adds the two times together: 4 + 6 = 10 — the slowest possible wrong answer, producing a combined time slower than either pump working alone, which is impossible. Pro tip: The combined rate method always works for these problems — convert each time to a rate (1/time), add the rates, then take the reciprocal to get the combined time. The answer must always be LESS than the faster pump's time alone. If your answer is slower than either individual pump, you've made an error.

Question 8

Carlos spends 13\frac{1}{3} of his budget on rent and 14\frac{1}{4} on groceries. He has $600 left. What is his total monthly budget?

  1. $1{,}028
  2. $1{,}200
  3. $1{,}440 (correct answer)
  4. $1{,}800

Explanation: This is a fractions and budget problem testing algebraic equation setup. Choice C ($1,440) is correct — spent fraction: 1/3 + 1/4 = 4/12 + 3/12 = 7/12. Remaining: 1 − 7/12 = 5/12. Set up: (5/12) × B = 600 → B = 600 × (12/5) = 600 × 2.4 = 1,440.ChoiceA(1,440. Choice A (1,028) divides $600 by the spent fraction instead of the remaining fraction: 600 ÷ (7/12) = 600 × (12/7) ≈ 1,028.ChoiceB(1,028. Choice B (1,200) treats the remaining fraction as 1/2 instead of 5/12: 600 × 2 = 1,200.ChoiceD(1,200. Choice D (1,800) treats the remaining fraction as 1/3: 600 × 3 = $1,800. Pro tip: When a fraction of a total is left over, the leftover fraction is (1 − sum of spent fractions). Here: 1 − (1/3 + 1/4) = 1 − 7/12 = 5/12. Then solve: (5/12) × Budget = 600 → Budget = 600 × (12/5) = 1,440. A quick check: 1/3 of 1,440 = 480, 1/4 of 1,440 = 360, 480 + 360 + 600 = 1,440 ✓.

Question 9

A bottle holds 750 ml of juice. If you pour out 150 ml, how much juice remains in the bottle?

  1. 500 ml
  2. 600 ml (correct answer)
  3. 550 ml
  4. 650 ml

Explanation: This problem asks how much juice remains after pouring some out. We need to subtract the amount poured from the original amount. Juice remaining = 750 ml - 150 ml = 600 ml. Choice C (550 ml) might result from an arithmetic error in subtraction.

Question 10

At a grocery store, apples cost $1.80 per pound. Maya buys 3.53.5 pounds of apples. Which expression represents the total cost of the apples (in dollars)?

  1. 1.80+3.51.80 + 3.5
  2. 3.5÷1.803.5 \div 1.80
  3. 1.80×3.51.80 \times 3.5 (correct answer)
  4. 1.80−3.51.80 - 3.5

Explanation: We need to find the total cost of apples when Maya buys 3.5 pounds at $1.80 per pound. To find the total cost when we know the price per unit and the number of units, we multiply: total cost = (price per pound) × (number of pounds). This gives us $1.80 × 3.5, which represents the total cost in dollars. Choice A incorrectly adds the price and weight, which doesn't give a meaningful result.