Advanced Percentage Applications

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Answer Key & Explanations

Advanced Percentage Applications · Grade 10 · Worksheet 2

1. Olivia is planning a fundraising event for her school's music program. She purchases 120 custom T-shirts from a supplier at a cost of $15 each. The supplier offers a 10% discount on the total cost for bulk orders. After receiving the shirts, Olivia decides to sell them at a 40% markup on the original cost per shirt (before the discount) to raise funds. However, due to low demand, she reduces the selling price by 25% during a flash sale. What is the final selling price of one T-shirt after the flash sale? Answer: 15.75 Solution: The original cost per shirt is $15. The markup is 40% on this cost, so the initial selling price before any discount is: $15 + (0.40 * $15) = $15 + $6 = $21.
   Full step-by-step solution

   Step 1: The original cost per shirt is $15. The markup is 40% on this cost, so the initial selling price before any discount is: $15 + (0.40 * $15) = $15 + $6 = $21. Step 2: During the flash sale, Olivia offers a 25% discount on the selling price of $21. The discount amount is: 0.25 * $21 = $5.25. Step 3: Subtract the discount from the selling price: $21 - $5.25 = $15.75. The final selling price of one T-shirt after the flash sale is $15.75.

2. Tane is a car salesperson at a dealership in Auckland. He earns a base salary of $2,400 per month plus a 7.5% commission on the total value of cars he sells. Last month, Tane sold three cars: a hatchback for $28,000, a sedan for $35,500, and an SUV for $52,000. How much did Tane earn in total last month? Answer: 11062.50 Solution: Find the total value of the cars sold. Total = $28,000 + $35,500 + $52,000 = $115,500. Calculate the commission.
   Full step-by-step solution

   Step 1: Find the total value of the cars sold. Total = $28,000 + $35,500 + $52,000 = $115,500. Step 2: Calculate the commission. Commission = 7.5% of $115,500 = 0.075 * 115,500 = $8,662.50. Step 3: Add the base salary to the commission. Total earnings = $2,400 + $8,662.50 = $11,062.50. The answer is 11062.50.

3. A laptop originally priced at $1200 is on sale for 25% off. If the sales tax is 8%, what is the final price? Answer: 972 Solution: Calculate the discount amount: 25% of $1200 = 0.25 × 1200 = $300 Calculate the sale price: $1200 - $300 = $900 Calculate the sales tax: 8% of $900 = 0.08 × 900 = $72 Calculate the final price: $900 + $72 = $972 The answer is 972.
   Full step-by-step solution

   Step 1: Calculate the discount amount: 25% of $1200 = 0.25 × 1200 = $300 Step 2: Calculate the sale price: $1200 - $300 = $900 Step 3: Calculate the sales tax: 8% of $900 = 0.08 × 900 = $72 Step 4: Calculate the final price: $900 + $72 = $972 The answer is 972.

4. Noah sells handmade furniture. He earns a 12% commission on all sales. Last month, his total sales were $8,500. How much commission did Noah earn? Answer: 1020 Solution: Identify the total sales and commission rate. Total sales = $8,500 Commission rate = 12% = 0.12 Calculate the commission.
   Full step-by-step solution

   Step 1: Identify the total sales and commission rate. Total sales = $8,500 Commission rate = 12% = 0.12 Step 2: Calculate the commission. Commission = Total sales × Commission rate Commission = $8,500 × 0.12 = $1,020 Noah earned $1,020 in commission.

5. Charlotte sells handmade candles. She sells a large candle for $72. The cost of materials for the candle is $27. Charlotte's markup is 62% of the cost. What is the selling price of the candle? Answer: 43.74 Solution: Identify the cost and markup percentage. Cost = $27 Markup percentage = 62% = 0.62 Calculate the markup amount. Markup = Cost × Markup percentage Markup = $27 × 0.62 = $16.74 Calculate the selling price.
   Full step-by-step solution

   Step 1: Identify the cost and markup percentage. Cost = $27 Markup percentage = 62% = 0.62 Step 2: Calculate the markup amount. Markup = Cost × Markup percentage Markup = $27 × 0.62 = $16.74 Step 3: Calculate the selling price. Selling price = Cost + Markup Selling price = $27 + $16.74 = $43.74 The selling price of the candle is $43.74.

6. Charlotte sells handmade candles. She sells a large candle for $72. If her commission rate is 12% of the sale price, how much commission does she earn from selling 7 such candles? Answer: 60.48 Solution: Commission per candle = 12% of $72 = 0.12 × 72 = $8.64 Total commission for 7 candles = 7 × $8.64 = $60.48 The answer is $60.48.
   Full step-by-step solution

   Step 1: Commission per candle = 12% of $72 = 0.12 × 72 = $8.64 Step 2: Total commission for 7 candles = 7 × $8.64 = $60.48 The answer is $60.48.

7. Mere is a sales consultant for a high-end electronics store. She earns a base salary of $1,800 per month plus a 7% commission on all sales over $4,000. Last month, her total sales were $26,000. How much did Mere earn in total last month? Answer: 3340 Solution: Calculate the sales amount eligible for commission: $26,000 - $4,000 = $22,000. Calculate the commission: 7% of $22,000 = 0.07 * $22,000 = $1,540. Add the base salary: $1,800 + $1,540 = $3,340.
   Full step-by-step solution

   Step 1: Calculate the sales amount eligible for commission: $26,000 - $4,000 = $22,000. Step 2: Calculate the commission: 7% of $22,000 = 0.07 * $22,000 = $1,540. Step 3: Add the base salary: $1,800 + $1,540 = $3,340. The answer is $3,340.

8. Sophia is a sales representative for a publishing company. She earns a base monthly salary of $2,800 plus a 6% commission on her total sales. In March, her total sales were $34,000. How much did Sophia earn in total for March? Answer: 4840 Solution: Identify the base salary: $2,800. Calculate the commission: 6% of $34,000 = 0.06 × 34,000 = $2,040. Add the base salary and commission: $2,800 + $2,040 = $4,840.
   Full step-by-step solution

   Step 1: Identify the base salary: $2,800. Step 2: Calculate the commission: 6% of $34,000 = 0.06 × 34,000 = $2,040. Step 3: Add the base salary and commission: $2,800 + $2,040 = $4,840. The answer is $4,840.