Word Problems - ACT Math

1. If a package of cookies contains 24 cookies and you eat 6, how many cookies are left?
   Answer: 18 This problem asks how many cookies remain after eating some. We need to subtract the eaten cookies from the original amount. Cookies remaining = 24 - 6 = 18 cookies. Choice C (20) might result from adding instead of subtracting, or making an arithmetic error.
2. A delivery driver is paid $18 per hour. On Monday, the driver worked 6.5 hours. What is the total pay for Monday?
   Answer: $117 We need to find the total pay for working 6.5 hours at $18 per hour. Total pay = (hourly rate) × (hours worked) = $18 × 6.5. This equals $18 × 6.5 = $117. Choice A ($24.50) appears to be an incorrect calculation, possibly dividing instead of multiplying.
3. A coffee shop sells muffins for $3 each. Jordan buys 4 muffins and pays with a $20 bill. How much change does Jordan receive?
   Answer: $8 We need to find how much change Jordan receives after buying 4 muffins at $3 each with a $20 bill. The total cost of the muffins is $4 \times 3 = 12$. To find the change, we subtract the total cost from the amount paid: $20 - 12 = 8$. Choice B ($12) represents the total cost of the muffins, not the change received.
4. If a box of pencils costs $4 and a notebook costs $3, how much do 2 boxes of pencils and 1 notebook cost?
   Answer: $11 This problem asks for the total cost of multiple different items. We calculate the cost of each item type separately, then add: (2 boxes of pencils × $4 per box) + (1 notebook × $3). This gives us $8 + $3 = $11. Choice C would result from incorrectly using $5 per box of pencils instead of $4 per box.
5. A streaming service costs $12 per month. A new subscriber gets a $5 discount on the first month only. What is the total cost for the first 3 months?
   Answer: $31 We need to find the total cost for 3 months when the service costs $12 per month with a $5 discount only on the first month. The first month costs $12 - 5 = 7$, and months 2 and 3 each cost $12. Total cost = $7 + 12 + 12 = 31$. Choice B ($36) would be the result if we forgot to apply the first-month discount.
6. A store sells rice for $0.90 per pound. If a bag costs $7.20, what is the weight of the bag in pounds?
   Answer: 8 pounds We need to find the weight of a rice bag that costs $7.20 when rice sells for $0.90 per pound. Using the formula $\text{weight} = \text{total cost} \div \text{price per pound}$: $\text{weight} = \$7.20 \div \$0.90 = 8$ pounds. Choice C (8.1 pounds) would result from a calculation error or misreading the decimal values.
7. A recipe uses $\tfrac{3}{4}$ cup of sugar per batch of muffins. If Lina makes $6$ batches, how much sugar does she need in total?
   Answer: $4\tfrac{1}{2}$ cups We need to find the total sugar needed for 6 batches when each batch uses 3/4 cup. To find the total, multiply the amount per batch by the number of batches: total sugar = 3/4 × 6. This equals 18/4 = 4 2/4 = 4 1/2 cups. Choice A (9/4) shows the improper fraction form before simplifying to the mixed number.
8. A company's weekly budget for office snacks is $60. If they already spent $18 this week, how much money is left in the snack budget?
   Answer: $42 We need to find how much money remains in a $60 weekly snack budget after spending $18. The remaining budget is $60 - 18 = 42$. Choice B ($78) would result from incorrectly adding $60 + 18$ instead of subtracting the amount spent.
9. A box contains 30 chocolates. If 12 are eaten, how many chocolates remain?
   Answer: 18 This problem asks how many chocolates remain after some are eaten. We need to subtract the eaten chocolates from the original amount. Chocolates remaining = 30 - 12 = 18 chocolates. Choice B (20) might result from an arithmetic error in subtraction.
10. At a grocery store, apples cost $1.80 per pound. Maya buys $3.5$ pounds of apples. Which expression represents the total cost of the apples (in dollars)?
    Answer: $1.80 \times 3.5$ 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.
11. A concert ticket costs $30. If you buy 3 tickets, what is the total cost?
    Answer: $90 This problem asks for the total cost of multiple identical items. We multiply the price per ticket by the number of tickets: total cost = $30 per ticket × 3 tickets. Calculating: $30 × 3 = $90. Choice C would result from incorrectly using $40 per ticket instead of $30 per ticket.
12. A train travels 300 miles in 5 hours. What is the average speed of the train in miles per hour?
    Answer: 60 mph This problem asks for the average speed of the train. We need to use the formula: speed = distance ÷ time. Average speed = 300 miles ÷ 5 hours = 60 mph. Choice D (60 mph) is marked as correct, which matches the calculation.
13. A classroom has 24 students. If each group can have at most 4 students, how many groups are needed?
    Answer: 6 groups This problem asks how many groups are needed when dividing students into groups of a maximum size. We divide the total number of students by the maximum group size: 24 students ÷ 4 students per group = 6 groups exactly. Since 24 divides evenly by 4, no partial group is needed. Choice C would result from incorrectly thinking we need an extra group for a remainder that doesn't exist.
14. A movie lasts 120 minutes. How many hours is the movie?
    Answer: 2 hours This problem asks to convert minutes to hours. We divide the number of minutes by 60 (since there are 60 minutes in an hour): time in hours = 120 minutes ÷ 60 minutes per hour. Calculating: 120 ÷ 60 = 2 hours. Choice B would result from incorrectly dividing by 80 instead of 60.
15. A school bus travels 120 miles to reach a destination. If it takes 2 hours, what is the speed of the bus?
    Answer: 60 mph This problem asks for the speed of the school bus. We need to use the formula: speed = distance ÷ time. Bus speed = 120 miles ÷ 2 hours = 60 mph. Choice B (55 mph) might result from an arithmetic error or misreading the problem.
16. A box contains 30 chocolates. If 10 chocolates are eaten, how many are left?
    Answer: 20 This problem asks how many items remain after some are removed. We subtract the number eaten from the original amount: remaining chocolates = $30 - 10 = 20$ chocolates. Choice C would result from incorrectly thinking 5 chocolates were eaten instead of 10 chocolates.
17. A classroom has $28$ students. The teacher forms groups with $4$ students in each group. How many groups can be formed?
    Answer: $7$ groups 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.
18. A movie theater sells tickets for $11 each. A group buys $t$ tickets and pays an additional $3 total service fee for the whole purchase. Which equation models the total cost $C$ in dollars?
    Answer: $C = 11t + 3$ We need to find an equation for the total cost C when buying t tickets at $11 each plus a $3 service fee for the entire purchase. The total cost equals the cost of tickets plus the one-time service fee: C = $11 × t + $3 = $11t + $3. Choice A incorrectly adds the service fee to the per-ticket price before multiplying by t.
19. A recipe requires 2 cups of flour for every 3 cups of sugar. How much flour is needed for 9 cups of sugar?
    Answer: 6 cups This problem asks how much flour is needed when scaling up a recipe proportionally. The ratio is 2 cups flour for every 3 cups sugar, so we set up the proportion: 2/3 = x/9, where x is the unknown flour amount. Cross-multiplying: 3x = 2 × 9 = 18, so x = 6 cups of flour. Choice A would result from incorrectly thinking the ratio is 1:3 instead of 2:3.
20. John has $150. If he spends $45 on a new shirt, how much money does he have left?
    Answer: $105 This problem asks how much money John has after making a purchase. We subtract the amount spent from the original amount: $\text{remaining money} = \text{starting money} - \text{amount spent}$. Calculating: $ 150 - 45 = 105 $. Choice A incorrectly subtracts $55 instead of $45, while choice C adds the amounts instead of subtracting.

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