Advanced Percentage Applications

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Answer Key & Explanations

Advanced Percentage Applications · Grade 10 · Worksheet 3

1. 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.

2. A principal of $2000 is invested at 8% annual interest compounded quarterly for 5 years. What is the final amount? (A = P(1 + r/n)^(nt)) Answer: 2971.89 Solution: P = 2000 (principal) r = 8% = 0.08 (annual interest rate) n = 4 (compounded quarterly) t = 5 (years) Apply the compound interest formula A = P(1 + r/n)^(nt) A = 2000(1 + 0.08/4)^(4×5) 0.08/4 = 0.02 1 + 0.02 = 1.02 4 × 5 = 20 Calculate (1.02)^20 (1.02)^20 = 1.485947 2000 × 1.485947 = 2971.894…
   Full step-by-step solution

   Step 1: Identify the values from the problem P = 2000 (principal) r = 8% = 0.08 (annual interest rate) n = 4 (compounded quarterly) t = 5 (years) Step 2: Apply the compound interest formula A = P(1 + r/n)^(nt) A = 2000(1 + 0.08/4)^(4×5) Step 3: Calculate inside the parentheses 0.08/4 = 0.02 1 + 0.02 = 1.02 Step 4: Calculate the exponent 4 × 5 = 20 Step 5: Calculate (1.02)^20 (1.02)^20 = 1.485947 Step 6: Multiply by the principal 2000 × 1.485947 = 2971.894 Step 7: Round to 2 decimal places for currency $2971.89 The final amount after 5 years is $2971.89.

3. Emma is a real estate agent who earns a commission of 3% on the first $150,000 of a house's selling price and 1.5% on the remaining amount. She sells a house for $375,000. How much total commission does Emma earn? Answer: $7,875 Solution: Calculate commission on the first $150,000 at 3%: 0.03 × $150,000 = $4,500. Calculate the remaining selling price: $375,000 - $150,000 = $225,000.
   Full step-by-step solution

   Step 1: Calculate commission on the first $150,000 at 3%: 0.03 × $150,000 = $4,500. Step 2: Calculate the remaining selling price: $375,000 - $150,000 = $225,000. Step 3: Calculate commission on the remaining $225,000 at 1.5%: 0.015 × $225,000 = $3,375. Step 4: Add the two commissions: $4,500 + $3,375 = $7,875. The answer is $7,875.

4. Ava sells handmade candles. She buys materials for $320 and sells the finished candles for $560. What is her percentage markup on cost? Answer: 75 Solution: Find the markup amount: $560 - $320 = $240 Divide the markup by the cost: $240 / $320 = 0.75 Convert to a percentage: 0.75 × 100 = 75% The percentage markup on cost is 75%.
   Full step-by-step solution

   Step 1: Find the markup amount: $560 - $320 = $240 Step 2: Divide the markup by the cost: $240 / $320 = 0.75 Step 3: Convert to a percentage: 0.75 × 100 = 75% The percentage markup on cost is 75%.

5. Ava sells handmade scarves. She buys materials for $18 per scarf and sells each for $45. If she sells 120 scarves in a month and her monthly expenses are $600, what is her total profit? Answer: 2640 Solution: Profit per scarf = Selling price - Cost = $45 - $18 = $27 Total profit from scarves = Profit per scarf × Number of scarves = $27 × 120 = $3240 Net profit = Total profit from scarves - Monthly expenses = $3240 - $600 = $2640 The total profit is $2640.
   Full step-by-step solution

   Step 1: Profit per scarf = Selling price - Cost = $45 - $18 = $27 Step 2: Total profit from scarves = Profit per scarf × Number of scarves = $27 × 120 = $3240 Step 3: Net profit = Total profit from scarves - Monthly expenses = $3240 - $600 = $2640 The total profit is $2640.

6. Mere bought a dress for $120 with a 30% discount and paid 8% sales tax. What was the final price? Answer: 90.72 Solution: Calculate the discount amount: 30% of $120 = 0.30 × 120 = $36 Calculate the discounted price: $120 - $36 = $84 Calculate the sales tax: 8% of $84 = 0.08 × 84 = $6.72 Add tax to discounted price: $84 + $6.72 = $90.72 The final price Mere paid was $90.72.
   Full step-by-step solution

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

7. Charlotte sells handmade jewelry. She purchases materials for $450 and spends an additional $120 on packaging. She wants a 40% markup on her total cost. What should be the selling price? Answer: 798 Solution: Calculate the total cost. Total cost = Cost of materials + Cost of packaging Total cost = $450 + $120 = $570 Calculate the markup amount.
   Full step-by-step solution

   Step 1: Calculate the total cost. Total cost = Cost of materials + Cost of packaging Total cost = $450 + $120 = $570 Step 2: Calculate the markup amount. Markup = Total cost × Markup percentage Markup = $570 × 40% = $570 × 0.40 = $228 Step 3: Calculate the selling price. Selling price = Total cost + Markup Selling price = $570 + $228 = $798 The selling price should be $798.

8. 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.

9. Kaia is a sales consultant for a home appliance store. She earns a base salary of $900 per week plus a commission of 12% on her total weekly sales. Last week, her total sales were $8,500. How much did Kaia earn in total last week? Answer: 1920 Solution: Calculate the commission earned. 12% of $8,500 = 0.12 x 8,500 = $1,020. Add the base salary to the commission.
   Full step-by-step solution

   Step 1: Calculate the commission earned. 12% of $8,500 = 0.12 x 8,500 = $1,020. Step 2: Add the base salary to the commission. $900 + $1,020 = $1,920. The answer is $1,920.