Percent Applications

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Answer Key & Explanations

Percent Applications · Grade 6 · Worksheet 3

1. Noah is organizing a school fundraiser and wants to raise $2,500 for new library books. On the first day, they raise 28% of their goal. On the second day, they raise an additional 35% of the original goal amount. What percentage of their fundraising goal have they achieved after both days? Answer: 63% Solution: Step 1: Calculate the percentage raised on the first day: 28% of the goal Step 2: Calculate the percentage raised on the second day: 35% of the goal Step 3: Add the two percentages together: 28% + 35% = 63% Step 4: Verify that 63% of $2,500 = 0.63 × 2500 = $1,575 The answer is 63%.
   Full step-by-step solution

   Step 1: Calculate the percentage raised on the first day: 28% of the goal Step 2: Calculate the percentage raised on the second day: 35% of the goal Step 3: Add the two percentages together: 28% + 35% = 63% Step 4: Verify that 63% of $2,500 = 0.63 × 2500 = $1,575 The answer is 63%.

2. Noah buys a new sofa for $1800. The store offers a 25% discount, and then charges 9% sales tax on the discounted price. What is the final price? Answer: 1471.50 Solution: Calculate the discount amount. 25% of $1800 = 0.25 × 1800 = $450. Subtract the discount from the original price.
   Full step-by-step solution

   Step 1: Calculate the discount amount. 25% of $1800 = 0.25 × 1800 = $450. Step 2: Subtract the discount from the original price. $1800 - $450 = $1350. This is the discounted price. Step 3: Calculate the sales tax on the discounted price. 9% of $1350 = 0.09 × 1350 = $121.50. Step 4: Add the tax to the discounted price. $1350 + $121.50 = $1471.50. The final price is $1471.50.

3. Noah is planning a school fundraiser and needs to order supplies. He found that 40% of the $1,200 budget will be used for food, 25% for decorations, and the rest for entertainment. If the entertainment costs increase by 15% due to unexpected fees, how much money will Noah need for entertainment after the increase? Answer: 483 Solution: Calculate the percentage of budget for entertainment Total budget = 100% Food = 40%, Decorations = 25% Entertainment = 100% - 40% - 25% = 35% 35% of $1,200 = 0.35 × 1,200 = $420 Calculate the 15% increase 15% of $420 = 0.15 × 420 = $63 $420 + $63 = $483 The answer is $483.
   Full step-by-step solution

   Step 1: Calculate the percentage of budget for entertainment Total budget = 100% Food = 40%, Decorations = 25% Entertainment = 100% - 40% - 25% = 35% Step 2: Calculate original entertainment cost 35% of $1,200 = 0.35 × 1,200 = $420 Step 3: Calculate the 15% increase 15% of $420 = 0.15 × 420 = $63 Step 4: Calculate final entertainment cost $420 + $63 = $483 The answer is $483.

4. Liam is shopping for a new video game that originally costs $48. The store is having a 25% off sale, and Liam also has a coupon for an additional 10% off the sale price. How much will Liam pay for the video game after both discounts are applied? Answer: 32.40 Solution: Find the sale price after 25% off. Original price = $48 25% discount means you pay 75% of the original price. Sale price = 48 × (75/100) = 48 × 0.75 = 36 So after the 25% discount, the price is $36.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Find the sale price after 25% off.** Original price = $48 25% discount means you pay 75% of the original price. Sale price = 48 × (75/100) = 48 × 0.75 = 36 So after the 25% discount, the price is $36. --- **Step 2: Apply the additional 10% off coupon to the sale price.** The coupon is 10% off the sale price, so you pay 90% of the sale price. Price after coupon = 36 × (90/100) = 36 × 0.90 = 32.40 --- **Step 3: State the final answer.** Liam will pay **$32.40** after both discounts.

5. Noah is planning a school fundraiser and needs to order supplies. The school has a budget of $1,500. He spends 35% of the budget on decorations, 25% on food, and 15% on prizes. The rest of the budget is for entertainment. How much money, in dollars, is left for entertainment? Answer: 375 Solution: Find the total percentage of the budget spent on decorations, food, and prizes. 35% + 25% + 15% = 75% Find the percentage of the budget left for entertainment. 100% - 75% = 25% Calculate 25% of the total budget ($1,500).
   Full step-by-step solution

   Step 1: Find the total percentage of the budget spent on decorations, food, and prizes. 35% + 25% + 15% = 75% Step 2: Find the percentage of the budget left for entertainment. 100% - 75% = 25% Step 3: Calculate 25% of the total budget ($1,500). 25% of $1,500 = (25/100) * 1500 = 0.25 * 1500 = 375 Step 4: State the final answer. The amount of money left for entertainment is $375.

6. A circular pizza with a diameter of 16 inches is cut into 8 equal slices. If you eat 3 slices, what percentage of the entire pizza have you consumed? (Use π = 3.14) Answer: 37.5 Solution: Find the area of the whole pizza. The pizza is a circle with diameter 16 inches, so the radius is half of that: radius = 16 / 2 = 8 inches. Area of a circle = π × radius².
   Full step-by-step solution

   Step 1: Find the area of the whole pizza. The pizza is a circle with diameter 16 inches, so the radius is half of that: radius = 16 / 2 = 8 inches. Area of a circle = π × radius². Using π = 3.14: Area = 3.14 × (8 × 8) = 3.14 × 64 = 200.96 square inches. Step 2: Understand the slices. The pizza is cut into 8 equal slices, so each slice is 1/8 of the total area. Step 3: Find the area of 3 slices. Area of 3 slices = 3 × (1/8 of total area) = 3/8 of total area. Step 4: Find the percentage of pizza eaten. Fraction eaten = 3/8. Percentage = (3/8) × 100. Step 5: Calculate the percentage. 3/8 = 0.375. 0.375 × 100 = 37.5%. Answer: 37.5