Percent Change

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Answer Key & Explanations

Percent Change · Grade 6 · Worksheet 3

1. Liam's favorite video game originally cost $60. During a holiday sale, the price was reduced by 25%. After the holidays, the store increased the sale price by 25% to return to the regular price. What is the final price of the video game after both changes? Answer: $56.25 Solution: Start with the original price. Original price = $60 Apply the 25% discount. 25% of $60 = (25/100) * 60 = 0.25 * 60 = $15 Sale price after discount = 60 - 15 = $45 Apply the 25% increase after the holidays.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Start with the original price.** Original price = $60 --- **Step 2: Apply the 25% discount.** 25% of $60 = (25/100) * 60 = 0.25 * 60 = $15 Sale price after discount = 60 - 15 = $45 --- **Step 3: Apply the 25% increase after the holidays.** Important: The 25% increase is applied to the sale price ($45), not the original price. 25% of $45 = (25/100) * 45 = 0.25 * 45 = $11.25 Price after increase = 45 + 11.25 = $56.25 --- **Step 4: Conclusion** The final price after both changes is $56.25. --- **Reasoning reminder:** Even though the discount and increase are both 25%, they are applied to different base amounts (first $60, then $45), so the final price is not the same as the original price.

2. A $1500 computer is discounted by 20% during a sale, then the sale price is increased by 10% for a restocking fee. What is the final price? Answer: $1320 Solution: Calculate the 20% discount amount: 20% of $1500 = 0.20 × 1500 = $300 Find the sale price: $1500 - $300 = $1200 Calculate the 10% restocking fee: 10% of $1200 = 0.10 × 1200 = $120 Add the restocking fee to the sale price: $1200 + $120 = $1320 The final price is $1320.
   Full step-by-step solution

   Step 1: Calculate the 20% discount amount: 20% of $1500 = 0.20 × 1500 = $300 Step 2: Find the sale price: $1500 - $300 = $1200 Step 3: Calculate the 10% restocking fee: 10% of $1200 = 0.10 × 1200 = $120 Step 4: Add the restocking fee to the sale price: $1200 + $120 = $1320 The final price is $1320.

3. A $2000 laptop is discounted by 25%, then the sale price is increased by 8% for tax. What is the final price? Answer: 1620 Solution: Calculate the 25% discount amount: 25% of $2000 = 0.25 × 2000 = $500 Subtract the discount from the original price: $2000 - $500 = $1500 Calculate the 8% tax amount: 8% of $1500 = 0.08 × 1500 = $120 Add the tax to the sale price: $1500 + $120 = $1620 The final price is $1620.
   Full step-by-step solution

   Step 1: Calculate the 25% discount amount: 25% of $2000 = 0.25 × 2000 = $500 Step 2: Subtract the discount from the original price: $2000 - $500 = $1500 Step 3: Calculate the 8% tax amount: 8% of $1500 = 0.08 × 1500 = $120 Step 4: Add the tax to the sale price: $1500 + $120 = $1620 The final price is $1620.

4. A store increased the price of a $120 item by 25%, then applied a 15% discount. What is the final price? Answer: 127.50 Solution: Start with the original price. Original price = 120 Apply the 25% price increase.
   Full step-by-step solution

   Let's solve this step by step. Step 1: Start with the original price. Original price = 120 Step 2: Apply the 25% price increase. A 25% increase means the new price is: 120 + (25% of 120) 25% of 120 = 25/100 * 120 = 0.25 * 120 = 30 So increased price = 120 + 30 = 150 Step 3: Apply the 15% discount to the increased price. A 15% discount means you pay 85% of the price. 85% of 150 = 85/100 * 150 = 0.85 * 150 0.85 * 150 = 127.50 Step 4: State the final price. Final price = 127.50 So the item's final price after the increase and then the discount is 127.50.

5. A $1500 computer is on sale for 20% off, then an additional 15% discount is applied at checkout. What is the final price? Answer: 1020 Solution: Calculate the first discount amount: 20% of $1500 = 0.20 × 1500 = $300 Calculate price after first discount: $1500 - $300 = $1200 Calculate the second discount amount: 15% of $1200 = 0.15 × 1200 = $180 Calculate final price: $1200 - $180 = $1020 The final price is $1020.
   Full step-by-step solution

   Step 1: Calculate the first discount amount: 20% of $1500 = 0.20 × 1500 = $300 Step 2: Calculate price after first discount: $1500 - $300 = $1200 Step 3: Calculate the second discount amount: 15% of $1200 = 0.15 × 1200 = $180 Step 4: Calculate final price: $1200 - $180 = $1020 The final price is $1020.

6. A rectangular garden is drawn on a coordinate plane with corners at (2,1), (8,1), (8,5), and (2,5). The gardener wants to increase the garden's area by 25% by extending only the length (the longer side). What will be the new coordinates of the corners that change position? Answer: (10,1) and (10,5) Solution: To solve percentage increase problems with geometric shapes, first find the original area. Then calculate the increased area by applying the percentage growth.
   Full step-by-step solution

   To solve percentage increase problems with geometric shapes, first find the original area. Then calculate the increased area by applying the percentage growth. When only one dimension changes, you can determine the new measurement by dividing the new area by the unchanged dimension. This demonstrates how percentage changes affect geometric measurements.

7. Noah's electronics store is having a clearance sale on laptops. A laptop originally priced at $1,250 is first marked down by 25%. Then, an additional 10% discount is applied for customers who pay in cash. What is the final price Noah pays for the laptop when he uses the cash payment option? Answer: $843.75 Solution: Calculate the first discount of 25% off $1,250 25% of $1,250 = 0.25 × 1,250 = $312.50 Price after first discount = $1,250 - $312.50 = $937.50 Calculate the additional 10% discount off the sale price 10% of $937.50 = 0.10 × 937.50 = $93.75 Final price = $937.50 - $93.75 = $843.75 The final price…
   Full step-by-step solution

   Step 1: Calculate the first discount of 25% off $1,250 25% of $1,250 = 0.25 × 1,250 = $312.50 Price after first discount = $1,250 - $312.50 = $937.50 Step 2: Calculate the additional 10% discount off the sale price 10% of $937.50 = 0.10 × 937.50 = $93.75 Final price = $937.50 - $93.75 = $843.75 The final price Noah pays for the laptop is $843.75.

8. Emma's school is planning a field trip and needs to raise $1,200 for transportation. So far, they have raised 65% of the total amount needed. The student council then organized a bake sale that raised an additional $280. What percentage of the total goal have they now reached? Answer: 88.33% Solution: Calculate the amount raised from the initial 65% 65% of $1,200 = 0.65 × 1,200 = $780 $780 + $280 = $1,060 Calculate what percentage $1,060 is of $1,200 (1,060 ÷ 1,200) × 100 = 0.8833 × 100 = 88.33% The answer is 88.33%.
   Full step-by-step solution

   Step 1: Calculate the amount raised from the initial 65% 65% of $1,200 = 0.65 × 1,200 = $780 Step 2: Add the bake sale money to find the total raised $780 + $280 = $1,060 Step 3: Calculate what percentage $1,060 is of $1,200 (1,060 ÷ 1,200) × 100 = 0.8833 × 100 = 88.33% The answer is 88.33%.