Advanced Percentage Applications

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Answer Key & Explanations

Advanced Percentage Applications · Grade 10 · Worksheet 2

1. Olivia is a sales consultant at a high-end electronics store. She earns a base salary of $2,400 per month plus a 7.5% commission on all sales she makes. In June, her total sales were $65,000. How much did Olivia earn in total for the month of June? Answer: 7275 Solution: Calculate the commission amount. 7.5% of $65,000 = 0.075 * 65,000 = $4,875. Step 2: Add the base salary to the commission.
   Full step-by-step solution

   Step 1: Calculate the commission amount. 7.5% of $65,000 = 0.075 * 65,000 = $4,875. Step 2: Add the base salary to the commission. $2,400 + $4,875 = $7,275. Olivia earned a total of $7,275 in June.

2. Tane is designing a rectangular sign for a store. The sign has a length of 24 cm and a width of 16 cm. A circular logo with a radius of 6 cm is placed exactly in the center of the sign. What percentage of the sign's area is NOT covered by the logo? (Use π = 3.14) Answer: 70.58 Solution: Find the area of the rectangular sign. Area = length × width = 24 × 16 = 384 square cm. Find the area of the circular logo.
   Full step-by-step solution

   Step 1: Find the area of the rectangular sign. Area = length × width = 24 × 16 = 384 square cm. Step 2: Find the area of the circular logo. Area = π × radius² = 3.14 × (6)² = 3.14 × 36 = 113.04 square cm. Step 3: Find the area not covered by the logo. Uncovered area = 384 - 113.04 = 270.96 square cm. Step 4: Calculate the percentage of the sign not covered. Percentage = (uncovered area / total area) × 100 = (270.96 / 384) × 100. Step 5: Divide 270.96 by 384 = 0.7058. Then multiply by 100 = 70.58%. The final answer is 70.58.

3. Mere bought a dress for $120 with a 30% discount and then paid 8% sales tax. What was the final price? Answer: 90.72 Solution: Discount = 30% of $120 = 0.30 × 120 = $36 Discounted price = Original price - Discount = $120 - $36 = $84 Sales tax = 8% of $84 = 0.08 × 84 = $6.72 Final price = Discounted price + Sales tax = $84 + $6.72 = $90.72 The final price Mere paid was $90.72.
   Full step-by-step solution

   Step 1: Calculate the discount amount Discount = 30% of $120 = 0.30 × 120 = $36 Step 2: Calculate the discounted price Discounted price = Original price - Discount = $120 - $36 = $84 Step 3: Calculate the sales tax Sales tax = 8% of $84 = 0.08 × 84 = $6.72 Step 4: Calculate the final price Final price = Discounted price + Sales tax = $84 + $6.72 = $90.72 The final price Mere paid was $90.72.

4. A laptop originally priced at $950 is discounted by 20% and then has 7% sales tax added. What is the final price? Answer: 813.20 Solution: 20% of $950 = 0.20 × 950 = $190 $950 - $190 = $760 7% of $760 = 0.07 × 760 = $53.20 $760 + $53.20 = $813.20 The final price is $813.20.
   Full step-by-step solution

   Step 1: Calculate the discount amount 20% of $950 = 0.20 × 950 = $190 Step 2: Calculate the price after discount $950 - $190 = $760 Step 3: Calculate the sales tax amount 7% of $760 = 0.07 × 760 = $53.20 Step 4: Calculate the final price $760 + $53.20 = $813.20 The final price is $813.20.

5. Noah sells handmade furniture. He buys a table for $320 and applies a 45% markup. During a clearance sale, he offers a 20% discount on the marked-up price. What is the final selling price of the table? Answer: 371.20 Solution: Calculate the markup amount. Markup = 45% of $320 = 0.45 × 320 = $144. Step 2: Calculate the marked-up price.
   Full step-by-step solution

   Step 1: Calculate the markup amount. Markup = 45% of $320 = 0.45 × 320 = $144. Step 2: Calculate the marked-up price. Marked-up price = $320 + $144 = $464. Step 3: Calculate the discount amount on the marked-up price. Discount = 20% of $464 = 0.20 × 464 = $92.80. Step 4: Calculate the final selling price. Final price = $464 - $92.80 = $371.20. The final selling price is $371.20.

6. Mere bought a laptop originally priced at $850. The store offers a 20% student discount, and then charges 7% sales tax on the discounted price. What is the final price? Answer: 727.60 Solution: Discount = 20% of $850 = 0.20 × 850 = $170 Discounted price = Original price - Discount = $850 - $170 = $680 Tax = 7% of $680 = 0.07 × 680 = $47.60 Final price = Discounted price + Tax = $680 + $47.60 = $727.60 The final price Mere pays is $727.60.
   Full step-by-step solution

   Step 1: Calculate the discount amount Discount = 20% of $850 = 0.20 × 850 = $170 Step 2: Calculate the discounted price Discounted price = Original price - Discount = $850 - $170 = $680 Step 3: Calculate the sales tax Tax = 7% of $680 = 0.07 × 680 = $47.60 Step 4: Calculate the final price Final price = Discounted price + Tax = $680 + $47.60 = $727.60 The final price Mere pays is $727.60.

7. 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.