Advanced Percentage Applications

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Answer Key & Explanations

Advanced Percentage Applications · Grade 10 · Worksheet 3

1. Aroha sells handmade scarves. She buys materials for $45 per scarf and marks up the price by 35%. During a sale, she offers a 15% discount on the marked price. What is the final selling price of one scarf? Answer: 51.64 Solution: Calculate the markup amount. Markup = 35% of $45 = 0.35 × 45 = $15.75. Step 2: Find the marked price.
   Full step-by-step solution

   Step 1: Calculate the markup amount. Markup = 35% of $45 = 0.35 × 45 = $15.75. Step 2: Find the marked price. Marked price = Cost + Markup = $45 + $15.75 = $60.75. Step 3: Calculate the discount amount. Discount = 15% of $60.75 = 0.15 × 60.75 = $9.1125. Step 4: Find the final selling price. Final price = Marked price - Discount = $60.75 - $9.1125 = $51.6375. Rounding to the nearest cent gives $51.64. The final selling price is $51.64.

2. Sophia sells handmade furniture. She sells a dining table for $1200. Her commission rate is 8% on the first $8000 in sales and 12% on any sales above $8000. If this is her only sale this month, how much commission does she earn? Answer: 96 Solution: The sale amount is $1200, which is less than $8000. So only the first commission rate applies. Commission = 8% of $1200 = 0.08 × 1200 = $96.
   Full step-by-step solution

   Step 1: The sale amount is $1200, which is less than $8000. So only the first commission rate applies. Step 2: Commission = 8% of $1200 = 0.08 × 1200 = $96. The answer is $96.

3. Aroha bought a bicycle originally priced at $375 with a 15% discount and then paid 7% sales tax. What was the final price? Answer: 341.06 Solution: Discount = 15% of $375 = 0.15 × 375 = $56.25 Discounted price = Original price - Discount = $375 - $56.25 = $318.75 Tax = 7% of discounted price = 0.07 × $318.75 = $22.3125 Final price = Discounted price + Tax = $318.75 + $22.3125 = $341.0625 $341.0625 rounds to $341.06 The final price Aroha…
   Full step-by-step solution

   Step 1: Calculate the discount amount Discount = 15% of $375 = 0.15 × 375 = $56.25 Step 2: Calculate the discounted price Discounted price = Original price - Discount = $375 - $56.25 = $318.75 Step 3: Calculate the tax amount Tax = 7% of discounted price = 0.07 × $318.75 = $22.3125 Step 4: Calculate the final price Final price = Discounted price + Tax = $318.75 + $22.3125 = $341.0625 Step 5: Round to the nearest cent $341.0625 rounds to $341.06 The final price Aroha paid was $341.06.

4. A rectangular prism-shaped storage tank has dimensions of 8 meters in length, 7 meters in width, and 10 meters in height. The tank is being filled with water at a constant rate. After some time, the water level reaches a height of 7 meters. What percentage of the tank's total volume is filled with water? (Ignore the shape of the tank's interior; assume it is a perfect rectangular prism.) Answer: 70 Solution: Find the total volume of the tank. The formula for the volume of a rectangular prism is V = length * width * height. Total volume = 8 * 7 * 10 = 560 cubic meters.
   Full step-by-step solution

   Step 1: Find the total volume of the tank. The formula for the volume of a rectangular prism is V = length * width * height. Total volume = 8 * 7 * 10 = 560 cubic meters. Step 2: Find the volume of the water. The water fills the tank to a height of 7 meters, so the water's volume is length * width * water height = 8 * 7 * 7 = 392 cubic meters. Step 3: Find the percentage of the tank filled. Percentage = (water volume / total volume) * 100 = (392 / 560) * 100. Step 4: Simplify 392/560. Divide numerator and denominator by 56: 392/56 = 7, 560/56 = 10, so 392/560 = 7/10 = 0.7. Step 5: 0.7 * 100 = 70. The answer is 70.

5. Mere is looking at a rectangular prism-shaped display case at a museum. The base of the case is a rectangle with length 24 cm and width 18 cm. The case has a height of 40 cm. A 1 cm thick layer of special preservation gel is poured to cover the entire base of the case. What percentage of the total volume of the display case does the gel occupy? Answer: 2.5 Solution: Find the total volume of the display case. The formula for volume of a rectangular prism is V = length * width * height. V_total = 24 * 18 * 40 = 17280 cubic cm.
   Full step-by-step solution

   Step 1: Find the total volume of the display case. The formula for volume of a rectangular prism is V = length * width * height. V_total = 24 * 18 * 40 = 17280 cubic cm. Step 2: Find the volume of the gel. The gel covers the entire base, so its length is 24 cm and width is 18 cm. Its height is 1 cm. V_gel = 24 * 18 * 1 = 432 cubic cm. Step 3: Find what fraction of the total volume the gel occupies. Fraction = V_gel / V_total = 432 / 17280. Step 4: Simplify the fraction. Divide numerator and denominator by 432: 432 / 17280 = 1 / 40. Step 5: Convert to a percentage. (1 / 40) * 100 = 2.5%. The gel occupies 2.5% of the total volume of the display case.

6. 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.