Advanced Percentage Applications

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Answer Key & Explanations

Advanced Percentage Applications · Grade 10 · Worksheet 1

1. Hana is a sales consultant for a luxury car dealership. She earns a base salary of $2,400 per month plus a 6% commission on all sales she makes. Last month, Hana sold two cars: a sedan for $38,000 and an SUV for $52,000. How much did Hana earn in total last month? Answer: 7800 Solution: Find the total value of Hana's car sales. She sold a sedan for $38,000 and an SUV for $52,000. Total sales = $38,000 + $52,000 = $90,000.
   Full step-by-step solution

   Step 1: Find the total value of Hana's car sales. She sold a sedan for $38,000 and an SUV for $52,000. Total sales = $38,000 + $52,000 = $90,000. Step 2: Calculate the commission. 6% of $90,000 = 0.06 * $90,000 = $5,400. Step 3: Add the base salary to the commission. Total earnings = $2,400 + $5,400 = $7,800. The answer is $7,800.

2. A smartphone manufacturer finds that 15% of phones produced have a minor defect. If they implement a new quality control system that reduces defects by 40%, and they produce 2,500 phones per day, how many defective phones will they now produce daily? Answer: 225 Solution: Find the original number of defective phones per day. The defect rate is 15%, and they produce 2500 phones per day.
   Full step-by-step solution

   Step 1: Find the original number of defective phones per day. The defect rate is 15%, and they produce 2500 phones per day. Original defective phones = 15% of 2500 = (15/100) * 2500 = 0.15 * 2500 = 375 Step 2: Understand the effect of the new quality control system. The new system reduces defects by 40%. That means the number of defective phones is reduced by 40% of the original defective number. Reduction in defects = 40% of 375 = (40/100) * 375 = 0.40 * 375 = 150 Step 3: Calculate the new number of defective phones per day. New defective phones = Original defective phones − Reduction = 375 − 150 = 225 Final answer: 225 defective phones per day after implementing the new system.

3. Mason is looking at a diagram of a rectangular prism with dimensions 12 cm by 7 cm by 17 cm. The prism is made of a material that costs $2.70 per cubic centimeter. A 22% discount is applied to the total cost of the material. What is the final cost after the discount? Answer: 3008.808 Solution: Find the volume of the rectangular prism. Volume = length * width * height = 12 * 7 * 17. Multiply 12 * 7 = 84.
   Full step-by-step solution

   Step 1: Find the volume of the rectangular prism. Volume = length * width * height = 12 * 7 * 17. Multiply 12 * 7 = 84. Then 84 * 17 = 1428 cubic centimeters. Step 2: Find the total cost before discount. Cost per cubic centimeter = $2.70. Total cost = 1428 * 2.70. Multiply 1428 * 2 = 2856, and 1428 * 0.70 = 999.6, so total cost = 2856 + 999.6 = 3855.6 dollars. Step 3: Apply the 22% discount. A 22% discount means you pay 100% - 22% = 78% of the original cost. 78% as a decimal is 0.78. Final cost = 3855.6 * 0.78 = 3008.808 dollars. The final cost after the discount is $3008.808.

4. Mason is a furniture store manager who needs to price a new sofa. The wholesale cost of the sofa is $720. He applies a 32% markup to determine the initial selling price. During a clearance event, he offers a 22% discount on the initial selling price. What is the final price a customer pays for the sofa after the discount? Answer: 741.31 Solution: Calculate the markup amount. 32% of $720 = 0.32 * 720 = $230.40. Step 2: Find the initial selling price.
   Full step-by-step solution

   Step 1: Calculate the markup amount. 32% of $720 = 0.32 * 720 = $230.40. Step 2: Find the initial selling price. $720 + $230.40 = $950.40. Step 3: Calculate the discount amount. 22% of $950.40 = 0.22 * 950.40 = $209.088. Step 4: Subtract the discount from the initial selling price. $950.40 - $209.088 = $741.312. Step 5: Round to the nearest cent. $741.31. The answer is 741.31.

5. A car's value depreciates by 20% annually. If the original value was $25,000, what is its value after 3 years? Answer: 12800 Solution: Calculate the depreciation factor: 100% - 20% = 80% = 0.8 Apply this factor for 3 years: Value after 1 year = $25,000 × 0.8 = $20,000 Value after 2 years = $20,000 × 0.8 = $16,000 Value after 3 years = $16,000 × 0.8 = $12,800 Alternatively, use the compound formula: $25,000 × (0.8)^3 = $25,000 ×…
   Full step-by-step solution

   Step 1: Calculate the depreciation factor: 100% - 20% = 80% = 0.8 Step 2: Apply this factor for 3 years: Value after 1 year = $25,000 × 0.8 = $20,000 Step 3: Value after 2 years = $20,000 × 0.8 = $16,000 Step 4: Value after 3 years = $16,000 × 0.8 = $12,800 Step 5: Alternatively, use the compound formula: $25,000 × (0.8)^3 = $25,000 × 0.512 = $12,800 The final value is $12,800.

6. Hana is a sales consultant for a home appliance store. She earns a base salary of $2,400 per month plus a 4% commission on all sales over $8,000. Last month, her total sales were $26,000. How much did Hana earn in total last month? Answer: 3120 Solution: Find the sales amount that earns commission: $26,000 - $8,000 = $18,000. Calculate the commission: 4% of $18,000 = 0.04 * $18,000 = $720. Add the commission to the base salary: $2,400 + $720 = $3,120.
   Full step-by-step solution

   Step 1: Find the sales amount that earns commission: $26,000 - $8,000 = $18,000. Step 2: Calculate the commission: 4% of $18,000 = 0.04 * $18,000 = $720. Step 3: Add the commission to the base salary: $2,400 + $720 = $3,120. The answer is 3120.