Advanced Percentage Applications

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Answer Key & Explanations

Advanced Percentage Applications · Grade 10 · Worksheet 1

1. A pharmaceutical company is testing a new medication. The drug's effectiveness decreases by 15% each hour in the bloodstream. If a patient takes a 200 mg dose, what percentage of the original dose remains active after 4 hours? Round your answer to the nearest whole percent. Answer: 52 Solution: The drug loses 15% effectiveness each hour, meaning 85% remains active after each hour.
   Full step-by-step solution

   Step 1: The drug loses 15% effectiveness each hour, meaning 85% remains active after each hour. Step 2: After 1 hour: 200 × 0.85 = 170 mg remains Step 3: After 2 hours: 170 × 0.85 = 144.5 mg remains Step 4: After 3 hours: 144.5 × 0.85 = 122.825 mg remains Step 5: After 4 hours: 122.825 × 0.85 = 104.40125 mg remains Step 6: Calculate percentage of original dose: (104.40125 ÷ 200) × 100 = 52.200625% Step 7: Round to nearest whole percent: 52% The answer is 52.

2. Charlotte is a real estate agent who earns a 4.5% commission on the first $150,000 of a home's sale price and a 2.75% commission on any amount above $150,000. She sells a home for $385,000. What is her total commission from this sale? Answer: 13212.5 Solution: Calculate commission on the first $150,000 at 4.5%. 4.5% of $150,000 = 0.045 * 150,000 = $6,750. Calculate the amount above $150,000.
   Full step-by-step solution

   Step 1: Calculate commission on the first $150,000 at 4.5%. 4.5% of $150,000 = 0.045 * 150,000 = $6,750. Step 2: Calculate the amount above $150,000. $385,000 - $150,000 = $235,000. Step 3: Calculate commission on the amount above $150,000 at 2.75%. 2.75% of $235,000 = 0.0275 * 235,000 = $6,462.50. Step 4: Add the two commissions together. $6,750 + $6,462.50 = $13,212.50. The answer is 13212.5.

3. Emma owns a boutique clothing store. She purchases a designer dress from a supplier for $240. She applies a 45% markup to set the initial selling price. During a clearance event, she offers a 30% discount on the marked-up price. After the event, she sells the remaining dresses at a final price that is 20% lower than the clearance price. What is the final price a customer pays for the dress? Answer: 194.88 Solution: Calculate the markup amount. 45% of $240 = 0.45 x 240 = $108. Step 2: Find the initial selling price after markup: $240 + $108 = $348.
   Full step-by-step solution

   Step 1: Calculate the markup amount. 45% of $240 = 0.45 x 240 = $108. Step 2: Find the initial selling price after markup: $240 + $108 = $348. Step 3: Calculate the clearance discount amount. 30% of $348 = 0.30 x 348 = $104.40. Step 4: Find the clearance price: $348 - $104.40 = $243.60. Step 5: Calculate the final reduction amount. 20% of $243.60 = 0.20 x 243.60 = $48.72. Step 6: Find the final price: $243.60 - $48.72 = $194.88. The answer is $194.88.

4. Noah is a car salesman at a dealership. He earns a base salary of $2,800 per month plus a 6% commission on the total value of cars he sells. Last month, Noah sold a total of $34,000 worth of cars. How much did Noah earn in total last month? Answer: 4840 Solution: Calculate the commission earned on sales. Commission = 6% of $34,000 = 0.06 * 34,000 = $2,040 Add the commission to the base salary.
   Full step-by-step solution

   Step 1: Calculate the commission earned on sales. Commission = 6% of $34,000 = 0.06 * 34,000 = $2,040 Step 2: Add the commission to the base salary. Total earnings = Base salary + Commission = $2,800 + $2,040 = $4,840 The answer is $4,840.

5. 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.

6. Liam invests $2,500 in a savings account that offers a 3.5% annual interest rate, compounded quarterly. He plans to leave the money untouched for 5 years. What will be the total amount in his account at the end of this period, rounded to the nearest cent? Answer: $2971.71 Solution: A = P * (1 + r/n)^(n*t) A = final amount P = principal (initial amount) = $2,500 r = annual interest rate (decimal) = 3.5% = 0.035 n = number of times interest is compounded per year = 4 (quarterly) t = number of years = 5 A = 2500 * (1 + 0.035/4)^(4*5) First, compute r/n = 0.035 / 4 = 0.00875…
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Identify the compound interest formula** The formula for compound interest is: A = P * (1 + r/n)^(n*t) Where: A = final amount P = principal (initial amount) = $2,500 r = annual interest rate (decimal) = 3.5% = 0.035 n = number of times interest is compounded per year = 4 (quarterly) t = number of years = 5 --- **Step 2: Substitute the values into the formula** A = 2500 * (1 + 0.035/4)^(4*5) --- **Step 3: Simplify inside the parentheses** First, compute r/n = 0.035 / 4 = 0.00875 So, 1 + r/n = 1 + 0.00875 = 1.00875 --- **Step 4: Compute the exponent** n*t = 4 * 5 = 20 So we have: A = 2500 * (1.00875)^(20) --- **Step 5: Calculate (1.00875)^(20)** We can break it down: First, (1.00875)^2 = 1.00875 * 1.00875 = 1.017575 (approx, but let's keep more precision for accuracy) Better to compute step-by-step with more precision: Let’s compute exactly: 1.00875^2 = 1.0175755625 1.00875^4 = (1.0175755625)^2 = 1.035461 (approx) 1.00875^8 = (1.035461)^2 ≈ 1.072177 1.00875^16 = (1.072177)^2 ≈ 1.149165 Now multiply by 1.00875^4 to get 1.00875^20: 1.149165 * 1.035461 ≈ 1.188685 (More precise calculator value: 1.00875^20 = 1.188685...) --- **Step 6: Multiply by principal** A = 2500 * 1.188685 = 2971.7125 --- **Step 7: Round to nearest cent** $2971.71 --- **Final Answer:** $2971.71

7. Isabella works as a sales consultant for a luxury car dealership. She earns a base salary of $2,800 per month plus a 6.5% commission on the total value of cars she sells. Last month, she sold three vehicles: a sedan for $34,000, an SUV for $52,000, and a sports car for $89,000. How much was Isabella's total income for the month, including her base salary and commission? Answer: 14,175 Solution: Calculate total sales value: $34,000 + $52,000 + $89,000 = $175,000 Calculate commission: 6.5% of $175,000 = 0.065 * $175,000 = $11,375 Add base salary: $2,800 + $11,375 = $14,175 The answer is $14,175.
   Full step-by-step solution

   Step 1: Calculate total sales value: $34,000 + $52,000 + $89,000 = $175,000 Step 2: Calculate commission: 6.5% of $175,000 = 0.065 * $175,000 = $11,375 Step 3: Add base salary: $2,800 + $11,375 = $14,175 The answer is $14,175.

8. Isabella sells handmade jewelry. She buys materials for $320 and marks up the price by 40% to set the selling price. During a sale, she offers a 25% discount on the selling price. What is the final sale price? Answer: 336 Solution: Calculate the markup amount. Markup = 40% of $320 = 0.40 × 320 = $128. Step 2: Selling price = cost + markup = 320 + 128 = $448.
   Full step-by-step solution

   Step 1: Calculate the markup amount. Markup = 40% of $320 = 0.40 × 320 = $128. Step 2: Selling price = cost + markup = 320 + 128 = $448. Step 3: Calculate the discount amount. Discount = 25% of $448 = 0.25 × 448 = $112. Step 4: Final sale price = selling price - discount = 448 - 112 = $336. The final sale price is $336.