Percent of Quantity

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Answer Key & Explanations

Percent of Quantity · Grade 6 · Worksheet 3

1. Emma is shopping for a winter coat that originally costs $120. The store is having a 30% off sale on all outerwear. After the discount is applied, there is an additional 7% sales tax. How much will Emma pay for the coat, including tax? Answer: 89.88 Solution: Original price: $120 Discount percentage: 30% Discount amount = 120 × 0.30 = $36 Discounted price = Original price - Discount amount Discounted price = 120 - 36 = $84 Tax percentage: 7% Tax amount = 84 × 0.07 = $5.88 Final price = Discounted price + Tax amount Final price = 84 + 5.88 = $89.88…
   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 discounted price Discounted price = Original price - Discount amount Discounted price = 120 - 36 = $84 Step 3: Calculate the sales tax Tax percentage: 7% Tax amount = 84 × 0.07 = $5.88 Step 4: Calculate the final price Final price = Discounted price + Tax amount Final price = 84 + 5.88 = $89.88 The answer is $89.88.

2. 45% of 860 = ? Answer: 387 Solution: Step 1: Convert 45% to a decimal by dividing by 100: 45 ÷ 100 = 0.45 Step 2: Multiply the decimal by the total quantity: 0.45 × 860 Step 3: Calculate 0.45 × 860 = 387 Step 4: Verify: 10% of 860 is 86, so 40% is 4 × 86 = 344, and 5% is 43, so 344 + 43 = 387 The answer is 387.
   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 total quantity: 0.45 × 860 Step 3: Calculate 0.45 × 860 = 387 Step 4: Verify: 10% of 860 is 86, so 40% is 4 × 86 = 344, and 5% is 43, so 344 + 43 = 387 The answer is 387.

3. 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.

4. 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 vegetables, what is the area of the vegetable 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). From (2, 1) to (8, 1), the y-coordinate is the same, so the length along x is 8 − 2 = 6.
   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). From (2, 1) to (8, 1), the y-coordinate is the same, so the length along x is 8 − 2 = 6. From (2, 1) to (2, 5), the x-coordinate is the same, so the width along y is 5 − 1 = 4. Step 2: Calculate the total area of the garden. Area of rectangle = length × width = 6 × 4 = 24. Step 3: Find the area planted with vegetables. 40% of the garden is vegetables, so: Vegetable area = 40% of 24 = (40/100) × 24 = 0.4 × 24. Step 4: Perform the multiplication. 0.4 × 24 = 9.6. Step 5: State the final answer. The area of the vegetable section is 9.6.

5. A clothing store is having a clearance sale where all items are marked 40% off. Maya finds a jacket with an original price of $85. At the checkout, she also uses a coupon that gives her an additional 15% off the discounted price. How much will Maya pay for the jacket after both discounts are applied? Answer: 43.35 Solution: Calculate the first discount (40% off the original price) Original price: $85 40% of $85 = 0.40 × 85 = $34 Price after first discount: $85 - $34 = $51 Calculate the second discount (15% off the already discounted price) Discounted price: $51 15% of $51 = 0.15 × 51 = $7.65 Price after second…
   Full step-by-step solution

   Step 1: Calculate the first discount (40% off the original price) Original price: $85 40% of $85 = 0.40 × 85 = $34 Price after first discount: $85 - $34 = $51 Step 2: Calculate the second discount (15% off the already discounted price) Discounted price: $51 15% of $51 = 0.15 × 51 = $7.65 Price after second discount: $51 - $7.65 = $43.35 Maya will pay $43.35 for the jacket after both discounts are applied.

6. 35% of 880 = ? Answer: 308 Solution: Write the percentage as a decimal. 35% is the same as 35/100, which equals 0.35. Multiply the decimal by the whole quantity.
   Full step-by-step solution

   Step 1: Write the percentage as a decimal. 35% is the same as 35/100, which equals 0.35. Step 2: Multiply the decimal by the whole quantity. 0.35 × 880 = ? Step 3: Calculate the multiplication: 0.35 × 880 = 308. The answer is 308.

7. 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

8. Emma is shopping for a winter coat that originally costs $120. The store is having a 30% off sale on all coats. Additionally, Emma has a coupon that gives her an extra 15% off the sale price. How much will Emma pay for the coat after both discounts are applied? Answer: 71.40 Solution: Calculate the first discount (30% off the original price). 30% of $120 = 0.30 × 120 = $36 Subtract the first discount from the original price to find the sale price.
   Full step-by-step solution

   Step 1: Calculate the first discount (30% off the original price). 30% of $120 = 0.30 × 120 = $36 Step 2: Subtract the first discount from the original price to find the sale price. $120 - $36 = $84 Step 3: Calculate the second discount (15% off the sale price). 15% of $84 = 0.15 × 84 = $12.60 Step 4: Subtract the second discount from the sale price to find the final price. $84 - $12.60 = $71.40 Emma will pay $71.40 for the coat.