Percent of Quantity

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Answer Key & Explanations

Percent of Quantity · Grade 6 · Worksheet 3

1. Liam is shopping for a new video game that originally costs $48. The store is having a 25% off sale on all games. How much money will Liam save on the game with this discount? Answer: 12 Solution: The original price of the game is $48. The discount is 25% off. We need to find how much money Liam will save, which is the discount amount.
   Full step-by-step solution

   Step 1: Understand the problem. The original price of the game is $48. The discount is 25% off. We need to find how much money Liam will save, which is the discount amount. Step 2: Convert the percentage to a decimal. 25% means 25 per 100, so 25% = 25/100 = 0.25. Step 3: Calculate the discount amount. Discount amount = Original price × Discount rate Discount amount = 48 × 0.25 Step 4: Perform the multiplication. 48 × 0.25 = 48 × (25/100) = 48 × 1/4 = 48/4 = 12 Step 5: Interpret the result. The discount amount is $12. This means Liam will save $12 on the game. Final Answer: 12

2. A technology company surveyed 1,200 employees about their preferred work arrangement. The results showed that 35% prefer full-time remote work, 42% prefer a hybrid schedule, and the rest prefer full-time office work. How many employees prefer full-time office work? Answer: 276 Solution: Find the percentage of employees who prefer full-time office work Total percentage is always 100% Percentage for office work = 100% - 35% - 42% = 23% Calculate 23% of 1,200 employees 23% of 1,200 = (23/100) × 1,200 = 0.23 × 1,200 0.23 × 1,200 = 276 Therefore, 276 employees prefer full-time…
   Full step-by-step solution

   Step 1: Find the percentage of employees who prefer full-time office work Total percentage is always 100% Percentage for office work = 100% - 35% - 42% = 23% Step 2: Calculate 23% of 1,200 employees 23% of 1,200 = (23/100) × 1,200 = 0.23 × 1,200 Step 3: Multiply 0.23 × 1,200 = 276 Therefore, 276 employees prefer full-time office work.

3. 37.5% of 960 = ? Answer: 360 Solution: Convert 37.5% to a decimal by dividing by 100: 37.5 ÷ 100 = 0.375 Multiply the decimal by the total quantity: 0.375 × 960 Calculate 0.375 × 960 = 360 The answer is 360.
   Full step-by-step solution

   Step 1: Convert 37.5% to a decimal by dividing by 100: 37.5 ÷ 100 = 0.375 Step 2: Multiply the decimal by the total quantity: 0.375 × 960 Step 3: Calculate 0.375 × 960 = 360 The answer is 360.

4. 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

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. Liam is shopping for a new video game that originally costs $48. The store is having a 25% off sale. 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 Calculate the 25% discount amount. 25% of 48 = 25/100 × 48 = 0.25 × 48 = 12 Discount amount = $12 Subtract the discount from the original price.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Find the original price.** Original price = $48 --- **Step 2: Calculate the 25% discount amount.** 25% of 48 = 25/100 × 48 = 0.25 × 48 = 12 Discount amount = $12 --- **Step 3: Subtract the discount from the original price.** Discounted price = 48 − 12 = 36 --- **Step 4: Calculate the 5% sales tax on the discounted price.** 5% of 36 = 5/100 × 36 = 0.05 × 36 = 1.80 Sales tax = $1.80 --- **Step 5: Add the sales tax to the discounted price.** Final price = 36 + 1.80 = 37.80 --- **Final Answer:** Liam will pay **$37.80**.

7. A rectangular city park is drawn on a coordinate plane with corners at (50, 40), (150, 40), (150, 90), and (50, 90). The city plans to build a playground that will occupy 30% of the park's total area. If the playground will be a rectangle with the same width as the park, what will be the length of the playground in coordinate units? Answer: 15 Solution: Find the dimensions of the park using the coordinates. Width = 150 - 50 = 100 units Length = 90 - 40 = 50 units Calculate the total area of the park.
   Full step-by-step solution

   Step 1: Find the dimensions of the park using the coordinates. Width = 150 - 50 = 100 units Length = 90 - 40 = 50 units Step 2: Calculate the total area of the park. Area = width × length = 100 × 50 = 5000 square units Step 3: Calculate 30% of the park's area for the playground. Playground area = 30% of 5000 = 0.30 × 5000 = 1500 square units Step 4: Since the playground has the same width as the park (100 units), find its length. Playground length = playground area ÷ width = 1500 ÷ 100 = 15 units The playground will be 15 coordinate units long.

8. A school is planning a field trip for 320 students. The transportation company says they can only take 85% of the students on their buses due to capacity limits. How many students will need to find alternative transportation? Answer: 48 Solution: Calculate how many students can be transported on the buses 85% of 320 students = 0.85 × 320 = 272 students Subtract the number of students who can be transported from the total Total students = 320 Students who can be transported = 272 Students needing alternative transportation = 320 - 272 =…
   Full step-by-step solution

   Step 1: Calculate how many students can be transported on the buses 85% of 320 students = 0.85 × 320 = 272 students Step 2: Subtract the number of students who can be transported from the total Total students = 320 Students who can be transported = 272 Students needing alternative transportation = 320 - 272 = 48 The answer is 48 students.