Percent Applications

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Answer Key & Explanations

Percent Applications · Grade 6 · Worksheet 1

1. Ava buys a new sofa for $2400. The store offers a 25% discount, and then she must pay a 9% sales tax on the discounted price. What is the final price Ava pays? Answer: 1962 Solution: Calculate the discount amount. 25% of $2400 = 0.25 × 2400 = $600. Subtract the discount from the original price.
   Full step-by-step solution

   Step 1: Calculate the discount amount. 25% of $2400 = 0.25 × 2400 = $600. Step 2: Subtract the discount from the original price. $2400 - $600 = $1800. This is the discounted price. Step 3: Calculate the sales tax on the discounted price. 9% of $1800 = 0.09 × 1800 = $162. Step 4: Add the tax to the discounted price to find the final price. $1800 + $162 = $1962. The final price Ava pays is $1962.

2. Emma is shopping for a winter coat that originally costs $120. The store is having a 30% off sale, but she also has to pay 8% sales tax on the final discounted price. How much money will Emma need to pay for the coat? Answer: $90.72 Solution: Calculate the discount amount. 30% of $120 = 0.30 × 120 = $36 Subtract the discount from the original price. $120 - $36 = $84 Calculate the sales tax on the discounted price.
   Full step-by-step solution

   Step 1: Calculate the discount amount. 30% of $120 = 0.30 × 120 = $36 Step 2: Subtract the discount from the original price. $120 - $36 = $84 Step 3: Calculate the sales tax on the discounted price. 8% of $84 = 0.08 × 84 = $6.72 Step 4: Add the tax to the discounted price. $84 + $6.72 = $90.72 The answer is $90.72.

3. Mere buys a new sofa for $2400. The store offers a 25% discount, and then she must pay 9% sales tax on the discounted price. What is the final price Mere pays? Answer: 1962 Solution: Calculate the discount amount. 25% of $2400 = 0.25 × 2400 = $600. Subtract the discount from the original price.
   Full step-by-step solution

   Step 1: Calculate the discount amount. 25% of $2400 = 0.25 × 2400 = $600. Step 2: Subtract the discount from the original price. $2400 - $600 = $1800. This is the discounted price. Step 3: Calculate the sales tax on the discounted price. 9% of $1800 = 0.09 × 1800 = $162. Step 4: Add the tax to the discounted price. $1800 + $162 = $1962. The final price Mere pays is $1962.

4. A rectangular swimming pool is drawn on a coordinate plane with corners at (0, 0), (25, 0), (25, 15), and (0, 15). A circular hot tub with a diameter of 6 meters is placed in the pool with its center at point (12.5, 7.5). What percentage of the pool's area is occupied by the hot tub? (Use π = 3.14) Answer: 7.536 Solution: Calculate the area of the rectangular pool. The pool has length 25 m and width 15 m. Area of rectangle = length × width = 25 × 15 = 375 square meters.
   Full step-by-step solution

   Step 1: Calculate the area of the rectangular pool. The pool has length 25 m and width 15 m. Area of rectangle = length × width = 25 × 15 = 375 square meters. Step 2: Calculate the area of the circular hot tub. The hot tub has diameter 6 m, so radius = 6 ÷ 2 = 3 m. Area of circle = π × radius² = 3.14 × (3 × 3) = 3.14 × 9 = 28.26 square meters. Step 3: Calculate what percentage the hot tub area is of the pool area. Percentage = (Area of hot tub ÷ Area of pool) × 100% = (28.26 ÷ 375) × 100% Step 4: Perform the division: 28.26 ÷ 375 = 0.07536 Step 5: Multiply by 100%: 0.07536 × 100% = 7.536% The answer is 7.536.

5. Mason buys a new video game console for $372. The sales tax rate is 7%. How much does Mason pay in total, including tax? Answer: $398.04 Solution: Find the amount of tax. 7% of $372 = 0.07 × 372 = $26.04. Add the tax to the original price.
   Full step-by-step solution

   Step 1: Find the amount of tax. 7% of $372 = 0.07 × 372 = $26.04. Step 2: Add the tax to the original price. $372 + $26.04 = $398.04. Mason pays $398.04 in total.

6. A circular garden has a diameter of 14 meters. A stone path is being built around the outside of the garden, creating a larger circle with a radius that is 3 meters longer than the garden's radius. What is the area of just the stone path? (Use π = 3.14) Answer: 160.14 Solution: The diameter of the garden is 14 m. Radius of garden = diameter / 2 = 14 / 2 = 7 m. Find the radius of the larger circle (garden + path) The path adds 3 m to the garden's radius.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Find the radius of the garden** The diameter of the garden is 14 m. Radius of garden = diameter / 2 = 14 / 2 = 7 m. --- **Step 2: Find the radius of the larger circle (garden + path)** The path adds 3 m to the garden's radius. Radius of larger circle = 7 + 3 = 10 m. --- **Step 3: Find the area of the garden** Area of garden = π × (radius of garden)^2 = 3.14 × (7)^2 = 3.14 × 49 = 153.86 m². --- **Step 4: Find the area of the larger circle (garden + path)** Area of larger circle = π × (radius of larger circle)^2 = 3.14 × (10)^2 = 3.14 × 100 = 314 m². --- **Step 5: Find the area of just the stone path** Path area = Area of larger circle − Area of garden = 314 − 153.86 = 160.14 m². --- **Final Answer:** 160.14

7. Noah is shopping for a new laptop that originally costs $1,250. The store is having a 25% off sale. When Noah checks out, he also has to pay 8% sales tax on the final discounted price. How much money will Noah need to pay for the laptop after the discount and tax? Answer: $1012.50 Solution: Calculate the discount amount. 25% of $1,250 = 0.25 × 1,250 = $312.50 Calculate the discounted price. $1,250 - $312.50 = $937.50 Calculate the tax amount.
   Full step-by-step solution

   Step 1: Calculate the discount amount. 25% of $1,250 = 0.25 × 1,250 = $312.50 Step 2: Calculate the discounted price. $1,250 - $312.50 = $937.50 Step 3: Calculate the tax amount. 8% of $937.50 = 0.08 × 937.50 = $75 Step 4: Calculate the final price. $937.50 + $75 = $1,012.50 The answer is $1012.50.