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Percent Applications

Grade 6 · Ratios · Worksheet 1

  1. Mason buys a rectangular rug for his living room. The rug is drawn on a coordinate plane with corners at (0, 0), (12, 0), (12, 7), and (0, 7). A circular pattern with a diameter of 2 meters is embroidered in the center of the rug. If the rug costs $27 per square meter, what is the total cost of the rug? (Use π = 3.14) Answer: ______________
  2. A store offers a 30% discount on a $1800 laptop, then charges 7% sales tax on the discounted price. What is the final price? Answer: ______________
  3. A store offers a 25% discount on a $240 item, then charges 8% sales tax on the discounted price. What is the final price? Answer: ______________
  4. Liam is shopping for a new video game that originally costs $60. The store is having a 25% 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: ______________
  5. Emma is shopping for a new bicycle. The bicycle she wants costs $1,275. The store is offering a 15% discount on all bicycles. After the discount, Emma must pay an 8% sales tax on the discounted price. What is the final total cost of the bicycle? Answer: ______________
  6. 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: ______________
  7. 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: ______________
  8. Tane is looking at a rectangular store display window that is 120 cm wide and 90 cm tall. A circular sale sign with a diameter of 30 cm is placed exactly in the center of the window. What percentage of the window's area is covered by the sale sign? (Use π = 3.14) Answer: ______________
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Answer Key & Explanations

Percent Applications · Grade 6 · Worksheet 1

  1. Mason buys a rectangular rug for his living room. The rug is drawn on a coordinate plane with corners at (0, 0), (12, 0), (12, 7), and (0, 7). A circular pattern with a diameter of 2 meters is embroidered in the center of the rug. If the rug costs $27 per square meter, what is the total cost of the rug? (Use π = 3.14) Answer: 2268 Solution: Find the area of the rectangular rug. Length = 12 meters, Width = 7 meters. Area = length × width = 12 × 7 = 84 square meters.
    Full step-by-step solution

    Step 1: Find the area of the rectangular rug. Length = 12 meters, Width = 7 meters. Area = length × width = 12 × 7 = 84 square meters. Step 2: The problem asks for the total cost of the rug, not just the patterned part. The circular pattern is part of the rug, so the entire rug area is used. Step 3: Multiply the total area by the cost per square meter. Total cost = 84 × $27 = $2,268. The answer is $2,268.

  2. A store offers a 30% discount on a $1800 laptop, then charges 7% sales tax on the discounted price. What is the final price? Answer: 1348.20 Solution: 30% of $1800 = 0.30 × 1800 = $540 $1800 - $540 = $1260 7% of $1260 = 0.07 × 1260 = $88.20 $1260 + $88.20 = $1348.20 The final price is $1348.20.
    Full step-by-step solution

    Step 1: Calculate the discount amount 30% of $1800 = 0.30 × 1800 = $540 Step 2: Calculate the sale price after discount $1800 - $540 = $1260 Step 3: Calculate the sales tax 7% of $1260 = 0.07 × 1260 = $88.20 Step 4: Calculate the final price $1260 + $88.20 = $1348.20 The final price is $1348.20.

  3. A store offers a 25% discount on a $240 item, then charges 8% sales tax on the discounted price. What is the final price? Answer: 194.40 Solution: First, find the discount amount. The original price is $240 and the discount is 25%. 25% of 240 = 25/100 * 240 = 0.25 * 240 = 60.
    Full step-by-step solution

    First, find the discount amount. The original price is $240 and the discount is 25%. 25% of 240 = 25/100 * 240 = 0.25 * 240 = 60. So, the discount amount is $60. Now subtract the discount from the original price: Discounted price = 240 - 60 = 180. Next, calculate the sales tax on the discounted price. Tax rate is 8%. 8% of 180 = 8/100 * 180 = 0.08 * 180 = 14.40. Add the tax to the discounted price: Final price = 180 + 14.40 = 194.40. Therefore, the final price after discount and tax is $194.40.

  4. Liam is shopping for a new video game that originally costs $60. The store is having a 25% 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: 38.25 Solution: Find the sale price after 25% off. Original price = $60 25% off means you pay 75% of the original price.
    Full step-by-step solution

    Let's solve this step-by-step. **Step 1: Find the sale price after 25% off.** Original price = $60 25% off means you pay 75% of the original price. Sale price = 60 × (75/100) Sale price = 60 × 0.75 Sale price = 45 **Step 2: Apply the additional 15% off coupon to the sale price.** The coupon is 15% off the sale price, so you pay 85% of the sale price. Price after coupon = 45 × (85/100) Price after coupon = 45 × 0.85 **Step 3: Calculate 45 × 0.85** 45 × 0.85 = 45 × (85/100) First, 45 × 85 = 3825 Then divide by 100: 3825 / 100 = 38.25 **Step 4: State the final amount.** Liam will pay $38.25 for the video game.

  5. Emma is shopping for a new bicycle. The bicycle she wants costs $1,275. The store is offering a 15% discount on all bicycles. After the discount, Emma must pay an 8% sales tax on the discounted price. What is the final total cost of the bicycle? Answer: 1170.45 Solution: Calculate the discount amount. 15% of $1,275 = 0.15 × 1,275 = $191.25. Step 2: Find the discounted price.
    Full step-by-step solution

    Step 1: Calculate the discount amount. 15% of $1,275 = 0.15 × 1,275 = $191.25. Step 2: Find the discounted price. $1,275 - $191.25 = $1,083.75. Step 3: Calculate the sales tax on the discounted price. 8% of $1,083.75 = 0.08 × 1,083.75 = $86.70. Step 4: Add the tax to the discounted price. $1,083.75 + $86.70 = $1,170.45. The final total cost is $1,170.45.

  6. 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.

  7. 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.

  8. Tane is looking at a rectangular store display window that is 120 cm wide and 90 cm tall. A circular sale sign with a diameter of 30 cm is placed exactly in the center of the window. What percentage of the window's area is covered by the sale sign? (Use π = 3.14) Answer: 6.54 Solution: Find the area of the rectangular window. Width = 120 cm, Height = 90 cm. Area = 120 x 90 = 10,800 square cm.
    Full step-by-step solution

    Step 1: Find the area of the rectangular window. Width = 120 cm, Height = 90 cm. Area = 120 x 90 = 10,800 square cm. Step 2: Find the area of the circular sale sign. Diameter = 30 cm, so radius = 30 / 2 = 15 cm. Area = π x radius x radius = 3.14 x 15 x 15 = 3.14 x 225 = 706.5 square cm. Step 3: Calculate the percentage. Percentage = (area of sign / area of window) x 100 = (706.5 / 10,800) x 100. Step 4: Divide 706.5 by 10,800 = 0.06541666... Step 5: Multiply by 100 = 6.541666... Step 6: Round to two decimal places = 6.54% The answer is 6.54.