Percent of Quantity

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Answer Key & Explanations

Percent of Quantity · Grade 6 · Worksheet 1

1. A school is planning a field trip for 360 students. The transportation company says they can only provide buses that seat 45 students each. What percentage of the total student capacity would be used if they fill all available buses completely? Answer: 100% Solution: Identify the total number of students: 360 Identify the bus capacity: 45 students per bus Calculate how many buses are needed: 360 ÷ 45 = 8 buses Calculate the total capacity of all buses: 8 buses × 45 students per bus = 360 students Calculate the percentage used: (360 ÷ 360) × 100 = 1 × 100 =…
   Full step-by-step solution

   Step 1: Identify the total number of students: 360 Step 2: Identify the bus capacity: 45 students per bus Step 3: Calculate how many buses are needed: 360 ÷ 45 = 8 buses Step 4: Calculate the total capacity of all buses: 8 buses × 45 students per bus = 360 students Step 5: Calculate the percentage used: (360 ÷ 360) × 100 = 1 × 100 = 100% The answer is 100%.

2. Liam is shopping for a new video game that originally costs $48. The store is having a 25% off sale on all games. If there is also a 5% sales tax applied to the discounted price, how much money, in dollars, will Liam need to pay for the game? Answer: 37.80 Solution: Find the original price. Original price = $48 Apply the 25% discount. 25% of $48 = 25/100 × 48 = 0.25 × 48 = 12 Discount amount = $12 Price after discount = 48 − 12 = $36 Apply the 5% sales tax to the discounted price.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Find the original price.** Original price = $48 --- **Step 2: Apply the 25% discount.** 25% of $48 = 25/100 × 48 = 0.25 × 48 = 12 Discount amount = $12 Price after discount = 48 − 12 = $36 --- **Step 3: Apply the 5% sales tax to the discounted price.** 5% of $36 = 5/100 × 36 = 0.05 × 36 = 1.80 Tax amount = $1.80 --- **Step 4: Add tax to discounted price to get final price.** Final price = 36 + 1.80 = $37.80 --- **Final Answer:** 37.80

3. 25% of 480 = ? Answer: 120 Solution: We are asked to find 25% of 480. Understand that "percent" means "per hundred". So 25% means 25 per hundred, which can be written as 25/100.
   Full step-by-step solution

   We are asked to find 25% of 480. Step 1: Understand that "percent" means "per hundred". So 25% means 25 per hundred, which can be written as 25/100. Step 2: "Of" in mathematics usually means multiplication. So 25% of 480 means (25/100) × 480. Step 3: Simplify 25/100. 25/100 = 1/4. Step 4: Now compute (1/4) × 480. This is the same as 480 ÷ 4. Step 5: 480 ÷ 4 = 120. Step 6: Therefore, 25% of 480 is 120. Final answer: 120

4. A circular pizza with a diameter of 16 inches is divided into 8 equal slices. If 37.5% of the pizza is covered with pepperoni, how many complete slices have pepperoni? (Use π = 3.14) Answer: 3 Solution: Calculate the total number of slices: 8 slices Each slice represents 100% ÷ 8 = 12.5% of the pizza The pepperoni covers 37.5% of the pizza Divide the pepperoni percentage by the percentage per slice: 37.5% ÷ 12.5% = 3 Since we need complete slices, 3 complete slices have pepperoni The answer is 3.
   Full step-by-step solution

   Step 1: Calculate the total number of slices: 8 slices Step 2: Each slice represents 100% ÷ 8 = 12.5% of the pizza Step 3: The pepperoni covers 37.5% of the pizza Step 4: Divide the pepperoni percentage by the percentage per slice: 37.5% ÷ 12.5% = 3 Step 5: Since we need complete slices, 3 complete slices have pepperoni The answer is 3.

5. 35% of 960 = ? Answer: 336 Solution: Convert 35% to a decimal by dividing by 100: 35 ÷ 100 = 0.35 Multiply the decimal by the total quantity: 0.35 × 960 Calculate 0.35 × 960 = 336 The answer is 336.
   Full step-by-step solution

   Step 1: Convert 35% to a decimal by dividing by 100: 35 ÷ 100 = 0.35 Step 2: Multiply the decimal by the total quantity: 0.35 × 960 Step 3: Calculate 0.35 × 960 = 336 The answer is 336.

6. A technology company surveyed 1,200 employees about their preferred work arrangement. The results showed that 35% prefer full-time remote work, 45% prefer a hybrid schedule, and the rest prefer full-time office work. If the company plans to accommodate all preferences, what percentage of employees prefer full-time office work, and how many employees is that? Answer: 20% and 240 employees Solution: Find the percentage that prefer full-time office work Total percentage must equal 100% 35% (remote) + 45% (hybrid) = 80% 100% - 80% = 20% prefer full-time office work Calculate the number of employees who prefer full-time office work 20% of 1,200 employees = 0.20 × 1,200 0.20 × 1,200 = 240…
   Full step-by-step solution

   Step 1: Find the percentage that prefer full-time office work Total percentage must equal 100% 35% (remote) + 45% (hybrid) = 80% 100% - 80% = 20% prefer full-time office work Step 2: Calculate the number of employees who prefer full-time office work 20% of 1,200 employees = 0.20 × 1,200 0.20 × 1,200 = 240 employees Therefore, 20% of employees prefer full-time office work, which represents 240 employees.

7. 35% of 720 = ? Answer: 252 Solution: Convert 35% to a decimal by dividing by 100: 35 ÷ 100 = 0.35 Multiply the decimal by the total quantity: 0.35 × 720 Calculate 0.35 × 720 = 252 The answer is 252.
   Full step-by-step solution

   Step 1: Convert 35% to a decimal by dividing by 100: 35 ÷ 100 = 0.35 Step 2: Multiply the decimal by the total quantity: 0.35 × 720 Step 3: Calculate 0.35 × 720 = 252 The answer is 252.