- A school is arranging a field trip for 245 students. Each bus can hold a maximum of 48 students. All but one bus will be completely full. How many students will be on the bus that is not full?
Answer: 5
To find the number of students on the last bus, divide the total number of students by the bus capacity: 245 ÷ 48. Since 5 × 48 = 240, there will be 5 full buses. The remaining students are 245 - 240 = 5. So, 5 students will be on the last bus.
- A factory produces widgets in batches. Machine A produces 156 widgets per batch, Machine B produces 208 widgets per batch, and Machine C produces 234 widgets per batch. If the factory needs exactly 2,496 widgets, what is the minimum number of total batches needed using any combination of machines?
Answer: 11 total batches minimum
To minimize batches, use the most efficient machine (C) as much as possible. 2,496 ÷ 234 = 10 batches with remainder 156. We need 10 batches of Machine C (10 × 234 = 2,340) plus exactly 156 more widgets. Machine A produces exactly 156 per batch, so we need 1 more batch from Machine A. Total: 10 + 1 = 11 batches minimum. Choice A uses a less efficient combination. Choice C uses only Machine A (16 batches). Choice D is impossible since 10 × 234 = 2,340 < 2,496.
- Janice reads 25 pages of a book each day from Monday to Friday. On Saturday and Sunday, she reads 40 pages each day. How many pages does she read in three full weeks?
Answer: 615
First, calculate the pages read during one week. Weekdays: 5 days × 25 pages/day = 125 pages. Weekend: 2 days × 40 pages/day = 80 pages. Total per week: 125 + 80 = 205 pages. Finally, multiply the weekly total by the number of weeks: 205 pages/week × 3 weeks = 615 pages.
- A warehouse starts the week with 1,500 boxes. On Monday, it ships out 3 shipments of 120 boxes each. On Tuesday, it receives a delivery of 250 boxes. How many boxes are in the warehouse at the end of Tuesday?
Answer: 1,390
First, calculate the total number of boxes shipped out: 3 shipments × 120 boxes/shipment = 360 boxes. Next, subtract the shipped boxes from the starting amount: 1,500 - 360 = 1,140 boxes. Finally, add the boxes from the new delivery: 1,140 + 250 = 1,390 boxes.
- For a school fundraiser, a class sold 150 boxes of cookies at $5 per box and 200 candy bars at $2 per bar. The cost to purchase the cookies and candy was $475. How much profit did the class make?
Answer: $675
First, calculate the total revenue. Revenue from cookies: 150 × $5 = $750. Revenue from candy bars: 200 × $2 = $400. Total revenue: $750 + $400 = $1,150. Profit is total revenue minus total cost. Profit = $1,150 - $475 = $675.
- A car rental company has two locations. Location A rents 35 cars per day. Location B rents 28 cars per day. After 14 days, how many more cars has Location A rented than Location B?
Answer: 98
First, find the daily difference in rentals between the two locations: 35 - 28 = 7 cars per day. Then, multiply this daily difference by the number of days to find the total difference: 7 cars/day × 14 days = 98 cars.
- A taxi service charges a flat fee of $4 plus an additional $2 for every mile traveled. If a passenger's trip is 13 miles long, what is the total cost of the ride?
Answer: $30
First, calculate the cost based on the distance traveled: 13 miles × $2/mile = $26. Then, add the flat fee to this amount: $26 + $4 = $30. The total cost is $30.
- Mark is saving to buy a bicycle that costs $350. He already has $65 saved. If he earns $15 each week for mowing lawns, how many weeks will it take him to save enough money to buy the bicycle?
Answer: 19
First, determine how much more money Mark needs: $350 - $65 = $285. Next, divide the amount needed by his weekly earnings to find the number of weeks: $285 ÷ $15/week = 19 weeks.
- An auditorium has three seating sections. The main floor has 25 rows with 30 seats per row. The first balcony has 15 rows with 20 seats per row. The second balcony has 10 rows with 18 seats per row. What is the total seating capacity of the auditorium?
Answer: 1,230
Calculate the seats in each section and then add them together. Main floor: 25 × 30 = 750 seats. First balcony: 15 × 20 = 300 seats. Second balcony: 10 × 18 = 180 seats. Total capacity: 750 + 300 + 180 = 1,230 seats.
- A farmer has 256 apple trees. This year, each tree is expected to produce 115 apples. The farmer plans to pack the apples into bags containing 8 apples each. How many full bags of apples can the farmer expect to pack?
Answer: 3,680
First, calculate the total number of apples produced: 256 trees × 115 apples/tree = 29,440 apples. Next, divide the total number of apples by the number of apples per bag to find how many full bags can be packed: 29,440 ÷ 8 = 3,680 bags.
- A customer buys 4 notebooks at $3 each and a pack of pens for $7. If the customer pays with a $20 bill, how much change should they receive?
Answer: $1
First, calculate the total cost of the notebooks: 4 notebooks × $3/notebook = $12. Next, add the cost of the pens: $12 + $7 = $19. Finally, subtract the total cost from the amount paid to find the change: $20 - $19 = $1.
- A family of 4 is planning a trip to a museum. Individual tickets cost $22 each. A family pass for up to 5 people costs $75. How much money does the family save by buying the family pass instead of four individual tickets?
Answer: $13
First, calculate the total cost of buying individual tickets: 4 people × $22/person = $88. The cost of the family pass is $75. To find the savings, subtract the cost of the pass from the cost of individual tickets: $88 - $75 = $13.
- A farm has two fields of corn. The North Field produced 1,860 bushels of corn. The South Field produced 350 fewer bushels than the North Field. What was the total number of bushels produced by both fields combined?
Answer: 3,370
First, calculate the production of the South Field: 1,860 - 350 = 1,510 bushels. Then, add the production of both fields to find the total: 1,860 (North) + 1,510 (South) = 3,370 bushels.
- A bakery produces 15 trays of muffins, with 12 muffins on each tray. They sell 110 muffins and discard 8 that were burned. How many muffins are left?
Answer: 62
First, calculate the total number of muffins produced: 15 trays × 12 muffins/tray = 180 muffins. Next, find the total number of muffins removed (sold or discarded): 110 + 8 = 118. Finally, subtract the removed muffins from the total produced: 180 - 118 = 62 muffins left.
- Three friends agree to clean up a park that is 2,000 meters long. On the first day, Amy cleans 650 meters. On the second day, Ben cleans 725 meters. How many meters are left for Chloe to clean on the third day?
Answer: 625
First, find the total length cleaned by Amy and Ben: 650 meters + 725 meters = 1,375 meters. Then, subtract this amount from the total length of the park to find how much is left for Chloe: 2,000 meters - 1,375 meters = 625 meters.
- A parking garage charges 3forthefirsthourand2 for each additional hour or part thereof. If Maria pays $$17 total, what is the maximum number of complete hours she could have parked?
Answer: 8 complete hours maximum
After paying $3 for the first hour, Maria has $17 - $3 = $14 remaining. Each additional hour costs $2, so $14 ÷ $2 = 7 additional hours. Total time: 1 + 7 = 8 complete hours. Since she pays for 'part thereof,' if she stayed 8 hours and 1 minute, she'd pay for 9 hours total, costing $3 + (8 × $2) = $19. At exactly 8 hours, she pays $17. Choice B miscounts by excluding the first hour. Choice C would cost $19. Choice D doesn't answer what was asked.
- An office buys 5 boxes of pens. Each box contains 12 packages, and each package holds 10 pens. If the office has 38 employees and gives each employee 15 pens, how many pens will be left over?
Answer: 30
First, find the total number of pens purchased: 5 boxes × 12 packages/box × 10 pens/package = 600 pens. Next, find the total number of pens given to employees: 38 employees × 15 pens/employee = 570 pens. Finally, subtract the pens given out from the total to find the number left over: 600 - 570 = 30 pens.
- A delivery truck makes stops at regular intervals. It starts with 847 packages and delivers the same number of packages at each stop. After 7 stops, it has 154 packages remaining. How many packages were delivered at the 5th stop?
Answer: 99 packages at the 5th stop
Packages delivered in 7 stops: 847 - 154 = 693 packages. Since the same number is delivered at each stop: 693 ÷ 7 = 99 packages per stop. At the 5th stop (and every other stop), exactly 99 packages were delivered. Choice B gives the total delivered through all 7 stops. Choice C gives total delivered through 5 stops (5 × 99 = 495). Choice D confuses remaining packages with packages delivered at one stop.
- A factory operates for 8 hours a day. It has 5 machines, and each machine produces 40 widgets per hour. At the end of one day, inspectors find that 75 widgets are defective. How many non-defective widgets were produced that day?
Answer: 1,525
First, calculate the total number of widgets produced by all machines in one hour: 5 machines × 40 widgets/hour = 200 widgets per hour. Next, calculate the total produced in an 8-hour day: 200 × 8 = 1,600 widgets. Finally, subtract the defective widgets: 1,600 - 75 = 1,525 non-defective widgets.
- A bookstore receives a shipment of 30 boxes of the same book. Each box contains 24 books. The total cost for the shipment was $9,360. What is the cost of a single book?
Answer: $13
First, find the total number of books in the shipment: 30 boxes × 24 books/box = 720 books. Next, divide the total cost of the shipment by the total number of books to find the cost per book: $9,360 ÷ 720 books = $13 per book.
