Percent Applications

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Answer Key & Explanations

Percent Applications · Grade 6 · Worksheet 3

1. Noah buys a new gaming console for $450. The store offers a 12% discount on the console, and then charges a 7% sales tax on the discounted price. What is the final price Noah pays? Answer: 423.72 Solution: Calculate the discount amount. 12% of $450 = 0.12 × 450 = $54. Subtract the discount from the original price.
   Full step-by-step solution

   Step 1: Calculate the discount amount. 12% of $450 = 0.12 × 450 = $54. Step 2: Subtract the discount from the original price. $450 - $54 = $396. This is the discounted price. Step 3: Calculate the sales tax on the discounted price. 7% of $396 = 0.07 × 396 = $27.72. Step 4: Add the tax to the discounted price. $396 + $27.72 = $423.72. The final price Noah pays is $423.72.

2. A rectangular city park is drawn on a coordinate plane with corners at (0, 0), (120, 0), (120, 80), and (0, 80). A circular fountain with a diameter of 20 meters is placed in the center of the park. What percentage of the park's area is occupied by the fountain? (Use π = 3.14) Answer: 3.27% Solution: Park length = 120 meters Park width = 80 meters Park area = length × width = 120 × 80 = 9,600 square meters Fountain diameter = 20 meters Fountain radius = diameter ÷ 2 = 20 ÷ 2 = 10 meters Fountain area = π × radius² = 3.14 × 10² = 3.14 × 100 = 314 square meters Calculate what percentage of the…
   Full step-by-step solution

   Step 1: Calculate the area of the rectangular park Park length = 120 meters Park width = 80 meters Park area = length × width = 120 × 80 = 9,600 square meters Step 2: Calculate the area of the circular fountain Fountain diameter = 20 meters Fountain radius = diameter ÷ 2 = 20 ÷ 2 = 10 meters Fountain area = π × radius² = 3.14 × 10² = 3.14 × 100 = 314 square meters Step 3: Calculate what percentage of the park is occupied by the fountain Percentage = (fountain area ÷ park area) × 100 Percentage = (314 ÷ 9,600) × 100 Percentage = 0.0327083 × 100 = 3.27083% Step 4: Round to two decimal places Percentage ≈ 3.27% The answer is 3.27%.

3. A circular pizza with a diameter of 16 inches is cut into 8 equal slices. If you eat 3 slices, what percentage of the whole pizza have you eaten? (Use π = 3.14) Answer: 37.5 Solution: We have a pizza cut into 8 equal slices. If you eat 3 slices, the fraction of the pizza eaten is 3/8. Fraction eaten = number of slices eaten / total slices = 3/8.
   Full step-by-step solution

   Step 1: Understand the problem We have a pizza cut into 8 equal slices. If you eat 3 slices, the fraction of the pizza eaten is 3/8. Step 2: Find the fraction eaten Fraction eaten = number of slices eaten / total slices = 3/8. Step 3: Convert fraction to percentage Percentage = (3/8) × 100. Step 4: Calculate 3/8 = 0.375 0.375 × 100 = 37.5 Step 5: Final answer You have eaten 37.5% of the pizza. Note: The diameter (16 inches) and π (3.14) are not needed here because the slices are equal, so the percentage depends only on the number of slices eaten out of the total slices.

4. A rectangular swimming pool is drawn on a coordinate plane with corners at (0, 0), (20, 0), (20, 12), and (0, 12). A triangular shallow end is marked off with vertices at (0, 0), (0, 12), and (8, 12). What percentage of the pool's total area is the shallow end? Answer: 20 Solution: Length = 20 units (from x=0 to x=20) Width = 12 units (from y=0 to y=12) Area of rectangle = length × width = 20 × 12 = 240 square units Base = 12 units (from y=0 to y=12) Height = 8 units (from x=0 to x=8) Area of triangle = (base × height) ÷ 2 = (12 × 8) ÷ 2 = 96 ÷ 2 = 48 square units Find…
   Full step-by-step solution

   Step 1: Find the area of the rectangular pool Length = 20 units (from x=0 to x=20) Width = 12 units (from y=0 to y=12) Area of rectangle = length × width = 20 × 12 = 240 square units Step 2: Find the area of the triangular shallow end Base = 12 units (from y=0 to y=12) Height = 8 units (from x=0 to x=8) Area of triangle = (base × height) ÷ 2 = (12 × 8) ÷ 2 = 96 ÷ 2 = 48 square units Step 3: Find what percentage the triangle is of the rectangle Fraction = triangle area ÷ rectangle area = 48 ÷ 240 = 0.2 Step 4: Convert to percentage Percentage = 0.2 × 100 = 20% The shallow end occupies 20% of the pool's total area.

5. A store offers a 30% discount on a $1800 laptop, then charges 7% sales tax on the discounted price. What is the final price? Answer: 1348.20 Solution: 30% of $1800 = 0.30 × 1800 = $540 $1800 - $540 = $1260 7% of $1260 = 0.07 × 1260 = $88.20 $1260 + $88.20 = $1348.20 The final price is $1348.20.
   Full step-by-step solution

   Step 1: Calculate the discount amount 30% of $1800 = 0.30 × 1800 = $540 Step 2: Calculate the sale price after discount $1800 - $540 = $1260 Step 3: Calculate the sales tax 7% of $1260 = 0.07 × 1260 = $88.20 Step 4: Calculate the final price $1260 + $88.20 = $1348.20 The final price is $1348.20.

6. Emma is shopping for a winter coat that originally costs $120. The store is having a 30% off sale, and Emma also has a coupon for an additional 10% off the sale price. How much will Emma pay for the coat after both discounts are applied? Answer: $75.60 Solution: Calculate the first discount (30% off original price) Original price: $120 30% of $120 = 0.30 × 120 = $36 Sale price after first discount: $120 - $36 = $84 Calculate the second discount (10% off sale price) Sale price: $84 10% of $84 = 0.10 × 84 = $8.40 Final price after second discount: $84 -…
   Full step-by-step solution

   Step 1: Calculate the first discount (30% off original price) Original price: $120 30% of $120 = 0.30 × 120 = $36 Sale price after first discount: $120 - $36 = $84 Step 2: Calculate the second discount (10% off sale price) Sale price: $84 10% of $84 = 0.10 × 84 = $8.40 Final price after second discount: $84 - $8.40 = $75.60 The answer is $75.60.

7. A store offers a 30% discount on a $1200 laptop, then charges 8% sales tax on the discounted price. What is the final price? Answer: $907.20 Solution: Calculate the discount amount. 30% of $1200 = 0.30 × 1200 = $360. Subtract the discount from the original price.
   Full step-by-step solution

   Step 1: Calculate the discount amount. 30% of $1200 = 0.30 × 1200 = $360. Step 2: Subtract the discount from the original price. $1200 - $360 = $840. This is the discounted price. Step 3: Calculate the sales tax on the discounted price. 8% of $840 = 0.08 × 840 = $67.20. Step 4: Add the tax to the discounted price to find the final price. $840 + $67.20 = $907.20. The final price is $907.20.