Whole Number Operations - Accuplacer Arithmetic

1. Three friends collected aluminum cans. Maria collected 135 cans, Sam collected 98, and Chloe collected 112. They decided to combine their cans and bundle them in packs of 25. After making as many full bundles as possible, how many cans were left over?
   Answer: 20 First, find the total number of cans collected: $135 + 98 + 112 = 345$. Next, divide the total by the pack size to find how many full bundles can be made and what the remainder is: $345 \div 25$. Since $25 \times 13 = 325$, there are 13 full bundles. The number of cans left over is the remainder: $345 - 325 = 20$.
2. Printer A can print 480 pages in 8 minutes. Printer B can print 630 pages in 9 minutes. What is the difference in the number of pages printed per minute between the two printers?
   Answer: 10 First, find the printing rate for each printer in pages per minute. Printer A's rate is $480 \div 8 = 60$ pages per minute. Printer B's rate is $630 \div 9 = 70$ pages per minute. Next, find the difference between their rates: $70 - 60 = 10$ pages per minute.
3. A construction project requires 2,184 concrete blocks. The blocks are delivered on pallets, with 24 blocks per pallet. Pallets are transported on trucks that can carry 9 pallets each. How many truck loads are needed to deliver all the blocks?
   Answer: 11 truck loads This is a multi-step division problem that tests your ability to work through real-world applications involving successive groupings. When you encounter problems like this, break them down into logical steps and be careful about rounding. First, you need to find how many pallets are required. Divide the total blocks by blocks per pallet: $2,184 ÷ 24 = 91$ pallets exactly. Next, determine how many truck loads are needed to transport 91 pallets. Since each truck carries 9 pallets: $91 ÷ 9 = 10.11...$ truck loads. Here's the crucial insight: you can't have a partial truck load in real life. Since you need 10.11 truck loads, you must round up to 11 complete truck loads to transport all the pallets. Looking at the wrong answers: Choice A (10 truck loads) represents the mistake of rounding down—10 trucks would only carry 90 pallets, leaving 1 pallet behind. Choice B (13 truck loads) is too high and might result from calculation errors in the division steps. Choice C (12 truck loads) is also excessive and could come from incorrectly rounding up too far or making arithmetic mistakes. The correct answer is D (11 truck loads). Study tip: In real-world math problems involving transportation, packaging, or capacity, always round up when you get a decimal result. You can't have partial trucks, boxes, or containers—if you need even a small fraction more, you need one complete additional unit.
4. An employee earns $18 per hour for the first 40 hours worked in a week and $27 per hour for any overtime hours. If the employee worked 48 hours in one week, what were their total earnings?
   Answer: $936 First, calculate the earnings from the regular hours: $40 \text{ hours} \times \$18\text{/hour} = \$720$. Next, determine the number of overtime hours worked: $48 - 40 = 8$ hours. Then, calculate the earnings from overtime: $8 \text{ hours} \times \$27\text{/hour} = \$216$. Finally, add the regular and overtime earnings to find the total: $\$720 + \$216 = \$936$.
5. A factory produces 250 widgets every hour. In an 8-hour workday, 15 widgets were found to be defective and were discarded. How many non-defective widgets were produced during the workday?
   Answer: 1,985 First, calculate the total number of widgets produced in the 8-hour workday: $250 \times 8 = 2,000$. Next, subtract the number of defective widgets from the total: $2,000 - 15 = 1,985$.
6. A customer buys 3 pounds of apples at $2 per pound and 2 loaves of bread at $4 per loaf. If the customer pays with a $20 bill, how much change should they receive?
   Answer: $6 First, calculate the cost of the apples: $3 \times \$2 = \$6$. Next, calculate the cost of the bread: $2 \times \$4 = \$8$. Then, find the total cost of the purchase by adding these amounts: $\$6 + \$8 = \$14$. Finally, subtract the total cost from the amount paid to find the change: $\$20 - \$14 = \$6$.
7. A delivery truck makes stops at regular intervals. It travels 2,856 miles total and makes a stop every 42 miles, including stops at the beginning and end of the route. How many stops does the truck make?
   Answer: 69 stops total The truck travels 2,856 miles with stops every 42 miles. Number of intervals: 2,856 ÷ 42 = 68 intervals. Since there are stops at both the beginning and end, the number of stops is 68 + 1 = 69 stops. Choice A forgets to add the final stop. Choice B counts only intervals, not stops. Choice D incorrectly adds 2 to the number of intervals.
8. An auditorium has 1,200 seats, which are arranged into 3 sections. The first section has 450 seats. The other two sections have an equal number of seats. How many seats are in one of those two sections?
   Answer: 375 First, subtract the seats in the first section from the total number of seats to find how many seats are in the other two sections combined: $1,200 - 450 = 750$. Since these 750 seats are divided equally between two sections, divide by 2: $750 \div 2 = 375$. Each of the other two sections has 375 seats.
9. A baker uses 6 ounces of chocolate chips for each batch of cookies. A wholesale box contains 4 pounds of chocolate chips. If one pound is equal to 16 ounces, how many full batches of cookies can the baker make from one box?
   Answer: 10 First, convert the total weight of chocolate chips from pounds to ounces. Since 1 pound = 16 ounces, the box contains $4 \text{ pounds} \times 16 \text{ ounces/pound} = 64$ ounces. Next, divide the total number of ounces by the amount needed per batch: $64 \div 6$. This equals 10 with a remainder of 4. Since the question asks for the number of full batches, the answer is 10.
10. A student's scores on four tests were 88, 92, 85, and 91. To achieve an average score of 90 across five tests, what must the student score on the fifth test?
    Answer: 94 First, find the total score needed for an average of 90 over five tests: $90 \times 5 = 450$. Next, find the sum of the scores on the first four tests: $88 + 92 + 85 + 91 = 356$. Finally, subtract the current total from the desired total to find the score needed on the fifth test: $450 - 356 = 94$.
11. What is the value of the expression $1,500 - 4 \times 120 + 80$?
    Answer: 1,100 Following the order of operations, perform multiplication before addition and subtraction. First, calculate $4 \times 120 = 480$. The expression becomes $1,500 - 480 + 80$. Now, perform the operations from left to right. First subtract: $1,500 - 480 = 1,020$. Then add: $1,020 + 80 = 1,100$.
12. A water tank holding 4,000 gallons is draining at a rate of 8 gallons per minute. At the same time, a pump is adding water at a rate of 3 gallons per minute. How many gallons of water will be in the tank after 2 hours?
    Answer: 3,400 First, find the net rate of change in water volume. Since it's draining faster than it's filling, the net change is a loss: $8 - 3 = 5$ gallons per minute. Next, convert the time from hours to minutes: $2 \text{ hours} \times 60 \text{ minutes/hour} = 120$ minutes. Then, calculate the total water lost over that time: $5 \text{ gallons/minute} \times 120 \text{ minutes} = 600$ gallons. Finally, subtract the total loss from the initial amount: $4,000 - 600 = 3,400$ gallons.
13. After paying $13 for a movie ticket and spending an equal amount on each of 3 snacks, Mark had $10 left from the $50 he started with. How much did each snack cost?
    Answer: $9 First, determine the total amount of money Mark spent. He started with $50 and had $10 left, so he spent $\$50 - \$10 = \$40$. From this total, subtract the cost of the movie ticket to find out how much was spent on snacks: $\$40 - \$13 = \$27$. Since this amount was spent on 3 snacks, divide by 3 to find the cost of each snack: $\$27 \div 3 = \$9$.
14. A family starts a road trip with a budget of $2,500. They spend $450 on hotels, $375 on food, and $180 on fuel. They also bought souvenirs for $95. How much of their budget is remaining?
    Answer: $1,400 First, calculate the total amount spent by adding all the expenses: $\$450 + \$375 + \$180 + \$95 = \$1,100$. Next, subtract the total expenses from the initial budget to find the remaining amount: $\$2,500 - \$1,100 = \$1,400$.
15. A factory conveyor belt moves at a rate of 4 inches per second. How many inches does the belt move in one hour?
    Answer: 14,400 To find the total distance, you need to find the total number of seconds in one hour. There are 60 seconds in a minute and 60 minutes in an hour. So, the total number of seconds is $60 \times 60 = 3,600$ seconds. Now, multiply the rate by the total time: $4 \text{ inches/second} \times 3,600 \text{ seconds} = 14,400$ inches.
16. A parking garage charges $8 for the first hour and $5 for each additional hour. If someone pays $73 total, how many hours did they park?
    Answer: 14 hours total After paying $8 for the first hour, the remaining cost is $73 - $8 = $65. This $65 covers additional hours at $5 each: $65 ÷ $5 = 13 additional hours. Total parking time: 1 + 13 = 14 hours. Choice A counts only the additional hours. Choice C incorrectly adds an extra hour. Choice D results from calculation errors in the division step.
17. A customer orders 5 T-shirts at a price of $14 each and 3 pairs of socks at $4 each. There is a flat shipping fee of $7 for the entire order. What is the total cost of the order?
    Answer: $89 First, calculate the cost of the T-shirts: $5 \times \$14 = \$70$. Next, calculate the cost of the socks: $3 \times \$4 = \$12$. Add these costs to get the subtotal: $\$70 + \$12 = \$82$. Finally, add the shipping fee to the subtotal to find the total cost: $\$82 + \$7 = \$89$.
18. A school is taking 140 students on a field trip. Each bus can hold a maximum of 30 students. If each bus costs $120 to rent, what is the total cost to rent enough buses for all the students?
    Answer: $600 First, determine the number of buses needed. Divide the total number of students by the capacity of each bus: $140 \div 30 = 4$ with a remainder of 20. Since there are 20 students remaining, a fifth bus is required. Therefore, 5 buses are needed. Next, calculate the total cost by multiplying the number of buses by the cost per bus: $5 \times \$120 = \$600$.
19. A florist has 850 roses. She wants to make bouquets with 12 roses in each. After making as many full bouquets as possible, how many roses will she have left over?
    Answer: 10 This problem asks for the remainder of a division. Divide the total number of roses by the number of roses per bouquet: $850 \div 12$. We can calculate that $12 \times 70 = 840$. The difference between the total roses and the roses used is $850 - 840 = 10$. Therefore, 10 roses will be left over.
20. For a fundraiser, a team washed cars for 6 hours. During the first 2 hours, they washed 15 cars per hour. For the remaining 4 hours, they washed 20 cars per hour. How many cars did they wash in total?
    Answer: 110 This problem requires two steps. First, calculate the number of cars washed in each period. For the first 2 hours: $2 \times 15 = 30$ cars. For the remaining 4 hours: $4 \times 20 = 80$ cars. Second, add the amounts from both periods to find the total: $30 + 80 = 110$ cars.

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