Percent of Quantity

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Answer Key & Explanations

Percent of Quantity · Grade 6 · Worksheet 2

1. A school is organizing a field trip for 320 students. The transportation company says that 15% of the students will need to ride in vans while the rest can ride in buses. If each bus can hold 40 students, how many buses are needed for the trip? Answer: 7 Solution: 100% - 15% = 85% of students will ride buses 85% of 320 = 0.85 × 320 = 272 students 272 students ÷ 40 students per bus = 6.8 buses Since we can't have a partial bus, we need to round up 6.8 buses rounds up to 7 buses The answer is 7 buses.
   Full step-by-step solution

   Step 1: Find the percentage of students riding buses 100% - 15% = 85% of students will ride buses Step 2: Calculate how many students will ride buses 85% of 320 = 0.85 × 320 = 272 students Step 3: Determine how many buses are needed 272 students ÷ 40 students per bus = 6.8 buses Step 4: Since we can't have a partial bus, we need to round up 6.8 buses rounds up to 7 buses The answer is 7 buses.

2. A technology company surveyed 1,200 employees about their preferred remote work setup. The results showed that 35% prefer using laptops, 40% prefer desktop computers, and the rest prefer tablets. If the company needs to order equipment for an upcoming expansion that will add 300 new remote workers, how many desktop computers should they order to maintain the same preference distribution? Answer: 120 Solution: First, find what percentage of employees prefer desktop computers from the survey. The problem states 40% prefer desktop computers. The company is adding 300 new remote workers.
   Full step-by-step solution

   Step 1: First, find what percentage of employees prefer desktop computers from the survey. The problem states 40% prefer desktop computers. Step 2: The company is adding 300 new remote workers. We need to find 40% of 300 to determine how many desktop computers to order. Step 3: Calculate 40% of 300. To find a percentage of a number, multiply the number by the percentage as a decimal. 40% = 40/100 = 0.4 Step 4: Multiply: 300 × 0.4 = 120 Step 5: Therefore, the company should order 120 desktop computers for the new remote workers. The answer is 120.

3. A rectangular garden is drawn on a coordinate plane with corners at (2, 1), (8, 1), (8, 5), and (2, 5). If 40% of the garden area is planted with flowers, what is the area of the flower section? Answer: 9.6 Solution: Find the length and width of the rectangle. The points are (2, 1), (8, 1), (8, 5), and (2, 5). Notice that the y-coordinates of the bottom two points are 1, and the y-coordinates of the top two points are 5.
   Full step-by-step solution

   Step 1: Find the length and width of the rectangle. The points are (2, 1), (8, 1), (8, 5), and (2, 5). Notice that the y-coordinates of the bottom two points are 1, and the y-coordinates of the top two points are 5. So the height is 5 - 1 = 4 units. The x-coordinates of the left two points are 2, and the x-coordinates of the right two points are 8. So the width is 8 - 2 = 6 units. Step 2: Calculate the total area of the garden. Area of a rectangle = length × width. Area = 6 × 4 = 24 square units. Step 3: Find the area planted with flowers. 40% of the garden is flowers. 40% as a decimal is 0.40. Flower area = 0.40 × 24. Step 4: Perform the multiplication. 0.40 × 24 = 9.6 square units. Thus, the area of the flower section is 9.6.

4. A technology company is analyzing its workforce diversity. They have 1,200 employees total, with 45% working in engineering roles. Among the engineering staff, 60% are software engineers and the rest are hardware engineers. What percentage of the company's total workforce are hardware engineers? Answer: 18% Solution: Find the number of engineering employees: 45% of 1,200 = 0.45 × 1,200 = 540 employees Find what percentage of engineers are hardware engineers: 100% - 60% = 40% Find the number of hardware engineers: 40% of 540 = 0.40 × 540 = 216 employees Find what percentage of total workforce are hardware…
   Full step-by-step solution

   Step 1: Find the number of engineering employees: 45% of 1,200 = 0.45 × 1,200 = 540 employees Step 2: Find what percentage of engineers are hardware engineers: 100% - 60% = 40% Step 3: Find the number of hardware engineers: 40% of 540 = 0.40 × 540 = 216 employees Step 4: Find what percentage of total workforce are hardware engineers: (216 ÷ 1,200) × 100 = 0.18 × 100 = 18% The answer is 18%.

5. 45% of 840 = ? Answer: 378 Solution: Convert 45% to a decimal by dividing by 100: 45 ÷ 100 = 0.45 Multiply the decimal by the number: 0.45 × 840 Calculate 0.45 × 800 = 360 Calculate 0.45 × 40 = 18 Add the results: 360 + 18 = 378 Therefore, 45% of 840 is 378.
   Full step-by-step solution

   Step 1: Convert 45% to a decimal by dividing by 100: 45 ÷ 100 = 0.45 Step 2: Multiply the decimal by the number: 0.45 × 840 Step 3: Calculate 0.45 × 800 = 360 Step 4: Calculate 0.45 × 40 = 18 Step 5: Add the results: 360 + 18 = 378 Therefore, 45% of 840 is 378.

6. Mason is saving money to buy a new video game that costs $80. Mason has already saved 55% of the total cost. How much money has Mason saved so far? Answer: 44 Solution: The total cost of the video game is $80. Mason has saved 55% of that amount. To find 55% of $80, multiply: $80 × (55 ÷ 100) = $80 × 0.55 = $44.
   Full step-by-step solution

   Step 1: The total cost of the video game is $80. Step 2: Mason has saved 55% of that amount. Step 3: To find 55% of $80, multiply: $80 × (55 ÷ 100) = $80 × 0.55 = $44. So Mason has saved $44.

7. Emma is shopping for a winter coat that originally costs $120. The store is having a 30% off sale on all outerwear. After applying the discount, there is an additional 6% sales tax. How much will Emma pay for the coat, including tax? Answer: 89.04 Solution: Original price: $120 Discount percentage: 30% Discount amount = 120 × 0.30 = $36 Sale price = Original price - Discount amount Sale price = 120 - 36 = $84 Tax percentage: 6% Tax amount = 84 × 0.06 = $5.04 Final price = Sale price + Tax amount Final price = 84 + 5.04 = $89.04 Emma will pay $89.04…
   Full step-by-step solution

   Step 1: Calculate the discount amount Original price: $120 Discount percentage: 30% Discount amount = 120 × 0.30 = $36 Step 2: Calculate the sale price after discount Sale price = Original price - Discount amount Sale price = 120 - 36 = $84 Step 3: Calculate the sales tax Tax percentage: 6% Tax amount = 84 × 0.06 = $5.04 Step 4: Calculate the final price Final price = Sale price + Tax amount Final price = 84 + 5.04 = $89.04 Emma will pay $89.04 for the coat.

8. A school is planning a field trip for 240 students. The school buses can each carry 45 students. If 15% of the students will be traveling by car with their parents instead of taking the bus, how many buses are needed for the remaining students? Answer: 5 Solution: Calculate how many students will travel by car: 15% of 240 = 0.15 × 240 = 36 students Calculate how many students need bus transportation: 240 - 36 = 204 students Calculate how many buses are needed: 204 ÷ 45 = 4.533...
   Full step-by-step solution

   Step 1: Calculate how many students will travel by car: 15% of 240 = 0.15 × 240 = 36 students Step 2: Calculate how many students need bus transportation: 240 - 36 = 204 students Step 3: Calculate how many buses are needed: 204 ÷ 45 = 4.533... Step 4: Since we can't have a fraction of a bus, we round up to the next whole number: 5 buses Step 5: Verify: 4 buses would carry 4 × 45 = 180 students, which is not enough for 204 students. 5 buses can carry 5 × 45 = 225 students, which is sufficient. The school needs 5 buses.