Percent Applications

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Answer Key & Explanations

Percent Applications · Grade 6 · Worksheet 2

1. Noah buys a new sofa that costs $2400. The store offers a 25% discount, and then charges 9% sales tax on the discounted price. What is the final price? Answer: 1962 Solution: Calculate the discount amount. 25% of $2400 = 0.25 × 2400 = $600. Subtract the discount from the original price.
   Full step-by-step solution

   Step 1: Calculate the discount amount. 25% of $2400 = 0.25 × 2400 = $600. Step 2: Subtract the discount from the original price. $2400 - $600 = $1800. This is the discounted price. Step 3: Calculate the sales tax on the discounted price. 9% of $1800 = 0.09 × 1800 = $162. Step 4: Add the tax to the discounted price. $1800 + $162 = $1962. The final price is $1962.

2. Emma buys a new laptop for $1500. The store offers a 25% discount, and then she must pay 6% sales tax on the discounted price. What is the final price? Answer: 1192.5 Solution: Calculate the discount amount. 25% of $1500 = 0.25 × 1500 = $375. Subtract the discount from the original price.
   Full step-by-step solution

   Step 1: Calculate the discount amount. 25% of $1500 = 0.25 × 1500 = $375. Step 2: Subtract the discount from the original price. $1500 - $375 = $1125. This is the discounted price. Step 3: Calculate the sales tax on the discounted price. 6% of $1125 = 0.06 × 1125 = $67.50. Step 4: Add the tax to the discounted price to find the final price. $1125 + $67.50 = $1192.50. The final price is $1192.50.

3. Noah buys a new sofa for $1800. The store offers a 25% discount, and then charges 9% sales tax on the discounted price. What is the final price? Answer: 1471.50 Solution: Calculate the discount amount. 25% of $1800 = 0.25 × 1800 = $450. Subtract the discount from the original price.
   Full step-by-step solution

   Step 1: Calculate the discount amount. 25% of $1800 = 0.25 × 1800 = $450. Step 2: Subtract the discount from the original price. $1800 - $450 = $1350. This is the discounted price. Step 3: Calculate the sales tax on the discounted price. 9% of $1350 = 0.09 × 1350 = $121.50. Step 4: Add the tax to the discounted price. $1350 + $121.50 = $1471.50. The final price is $1471.50.

4. A store offers a 25% discount on a $120 item, then charges 8% sales tax on the discounted price. What is the final price? Answer: 97.20 Solution: Find the discount amount. The original price is $120. Discount rate is 25%, so the discount amount is: Discount = 25% of 120 = (25/100) × 120 = 0.25 × 120 = 30.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Find the discount amount.** The original price is $120. Discount rate is 25%, so the discount amount is: Discount = 25% of 120 = (25/100) × 120 = 0.25 × 120 = 30. --- **Step 2: Find the discounted price.** Discounted price = Original price − Discount = 120 − 30 = 90. --- **Step 3: Calculate sales tax on the discounted price.** Sales tax rate = 8%. Tax amount = 8% of 90 = (8/100) × 90 = 0.08 × 90 = 7.20. --- **Step 4: Find the final price.** Final price = Discounted price + Tax = 90 + 7.20 = 97.20. --- **Final answer:** 97.20

5. 25% of 1200 = ? Answer: 300 Solution: We are asked to find 25% of 1200. "Percent" means "per hundred," so 25% means 25 per 100. Convert 25% to a decimal.
   Full step-by-step solution

   Step 1: Understand the problem. We are asked to find 25% of 1200. "Percent" means "per hundred," so 25% means 25 per 100. Step 2: Convert 25% to a decimal. To convert a percentage to a decimal, divide by 100. 25% = 25 / 100 = 0.25 Step 3: Multiply the decimal by the number. We now calculate 0.25 times 1200. 0.25 × 1200 = ? Step 4: Break the multiplication into parts. 0.25 is the same as 1/4. So, 25% of 1200 = (1/4) × 1200. Step 5: Perform the multiplication. (1/4) × 1200 = 1200 / 4 1200 ÷ 4 = 300 Step 6: State the final answer. 25% of 1200 = 300

6. Aroha buys a new sofa that costs $2400. The store offers a 15% discount, and then she must pay a 9% sales tax on the discounted price. What is the final price Aroha pays? Answer: 2223.6 Solution: Calculate the discount amount. 15% of $2400 = 0.15 × 2400 = $360. Subtract the discount from the original price.
   Full step-by-step solution

   Step 1: Calculate the discount amount. 15% of $2400 = 0.15 × 2400 = $360. Step 2: Subtract the discount from the original price. $2400 - $360 = $2040. This is the discounted price. Step 3: Calculate the sales tax on the discounted price. 9% of $2040 = 0.09 × 2040 = $183.60. Step 4: Add the tax to the discounted price to find the final price. $2040 + $183.60 = $2223.60. The final price Aroha pays is $2223.60.

7. Liam is shopping for a new video game that normally costs $45. The store is having a 20% off sale, and Liam also has a coupon for an additional 15% off the sale price. How much will Liam pay for the video game? Answer: 30.60 Solution: Find the sale price after 20% off. The original price is $45. 20% off means you pay 80% of the original price.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Find the sale price after 20% off.** The original price is $45. 20% off means you pay 80% of the original price. 80% as a decimal is 0.80. Sale price = 45 × 0.80 Sale price = 36.00 So after the store's 20% discount, the price is $36.00. --- **Step 2: Apply the coupon for an additional 15% off the sale price.** The coupon takes 15% off the $36.00 sale price. That means you pay 85% of the sale price. 85% as a decimal is 0.85. Price after coupon = 36.00 × 0.85 --- **Step 3: Calculate the final price.** 36.00 × 0.85: First, 36 × 85: 36 × 80 = 2880 36 × 5 = 180 Add: 2880 + 180 = 3060 Now, since 0.85 has two decimal places, we adjust: 3060 ÷ 100 = 30.60 --- **Final Answer:** Liam will pay **$30.60**.

8. A laptop originally costs $1200. It's on sale for 25% off, and then you have a coupon for an additional 10% off the sale price. What is the final price? Answer: $810 Solution: Calculate the 25% discount on the original price 25% of $1200 = 0.25 × 1200 = $300 $1200 - $300 = $900 Calculate the additional 10% coupon discount on the sale price 10% of $900 = 0.10 × 900 = $90 $900 - $90 = $810 The final price is $810.
   Full step-by-step solution

   Step 1: Calculate the 25% discount on the original price 25% of $1200 = 0.25 × 1200 = $300 Step 2: Find the sale price after the first discount $1200 - $300 = $900 Step 3: Calculate the additional 10% coupon discount on the sale price 10% of $900 = 0.10 × 900 = $90 Step 4: Find the final price after both discounts $900 - $90 = $810 The final price is $810.

9. A store offers a 30% discount on a $250 item, then charges 8% sales tax on the discounted price. What is the final price? Answer: 189 Solution: Find the discount amount. The original price is $250, and the discount is 30%. Discount amount = 30% of 250 = (30/100) * 250 = 0.30 * 250 = 75.
   Full step-by-step solution

   Let's solve this step by step. Step 1: Find the discount amount. The original price is $250, and the discount is 30%. Discount amount = 30% of 250 = (30/100) * 250 = 0.30 * 250 = 75. Step 2: Subtract the discount from the original price to get the discounted price. Discounted price = 250 - 75 = 175. Step 3: Calculate the sales tax on the discounted price. Sales tax rate is 8%. Tax amount = 8% of 175 = (8/100) * 175 = 0.08 * 175 = 14. Step 4: Add the tax to the discounted price to get the final price. Final price = 175 + 14 = 189. So, the final price after discount and tax is $189.