Percent Change

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Answer Key & Explanations

Percent Change · Grade 6 · Worksheet 1

1. A $2400 refrigerator is discounted by 25% during a sale, then the sale price is increased by 8% for a restocking fee. What is the final price? Answer: 1944 Solution: Calculate the 25% discount amount: 25% of $2400 = 0.25 × 2400 = $600 Calculate the sale price: $2400 - $600 = $1800 Calculate the 8% restocking fee: 8% of $1800 = 0.08 × 1800 = $144 Calculate the final price: $1800 + $144 = $1944 The final price is $1944.
   Full step-by-step solution

   Step 1: Calculate the 25% discount amount: 25% of $2400 = 0.25 × 2400 = $600 Step 2: Calculate the sale price: $2400 - $600 = $1800 Step 3: Calculate the 8% restocking fee: 8% of $1800 = 0.08 × 1800 = $144 Step 4: Calculate the final price: $1800 + $144 = $1944 The final price is $1944.

2. A $2400 laptop is discounted by 25%, then the sale price is increased by 8% for tax. What is the final price? Answer: $1944 Solution: Calculate the 25% discount amount: 25% of $2400 = 0.25 × 2400 = $600 Subtract the discount from the original price: $2400 - $600 = $1800 Calculate the 8% tax amount: 8% of $1800 = 0.08 × 1800 = $144 Add the tax to the sale price: $1800 + $144 = $1944 The final price is $1944.
   Full step-by-step solution

   Step 1: Calculate the 25% discount amount: 25% of $2400 = 0.25 × 2400 = $600 Step 2: Subtract the discount from the original price: $2400 - $600 = $1800 Step 3: Calculate the 8% tax amount: 8% of $1800 = 0.08 × 1800 = $144 Step 4: Add the tax to the sale price: $1800 + $144 = $1944 The final price is $1944.

3. A $2000 laptop is discounted by 25% during a sale, then the sale price is increased by 8% for a restocking fee. What is the final price? Answer: 1620 Solution: Calculate the 25% discount amount: 25% of $2000 = 0.25 × 2000 = $500 Find the sale price: $2000 - $500 = $1500 Calculate the 8% restocking fee: 8% of $1500 = 0.08 × 1500 = $120 Add the restocking fee 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: Find the sale price: $2000 - $500 = $1500 Step 3: Calculate the 8% restocking fee: 8% of $1500 = 0.08 × 1500 = $120 Step 4: Add the restocking fee to the sale price: $1500 + $120 = $1620 The final price is $1620.

4. A $1500 computer is on sale for 20% off. After the discount, a 7% sales tax is applied. What is the final price? Answer: $1284 Solution: Calculate the discount amount: 20% of $1500 = 0.20 × 1500 = $300 Calculate the sale price: $1500 - $300 = $1200 Calculate the sales tax: 7% of $1200 = 0.07 × 1200 = $84 Add the tax to the sale price: $1200 + $84 = $1284 The final price is $1284.
   Full step-by-step solution

   Step 1: Calculate the discount amount: 20% of $1500 = 0.20 × 1500 = $300 Step 2: Calculate the sale price: $1500 - $300 = $1200 Step 3: Calculate the sales tax: 7% of $1200 = 0.07 × 1200 = $84 Step 4: Add the tax to the sale price: $1200 + $84 = $1284 The final price is $1284.

5. Liam's favorite video game was originally priced at $45. During a holiday sale, the price was reduced by 20%. After the holidays, the store increased the sale price by 20% to return to the regular price. What is the final price of the video game after both changes? Answer: $43.20 Solution: The original price is $45. 80% as a decimal is 0.80. So, sale price = 45 × 0.80.
   Full step-by-step solution

   Let's go step-by-step. --- **Step 1: Original price** The original price is $45. --- **Step 2: Apply the 20% discount** A 20% discount means you pay 80% of the original price. 80% as a decimal is 0.80. So, sale price = 45 × 0.80. Calculation: 45 × 0.80 = 36. So after the discount, the price is $36. --- **Step 3: Apply the 20% increase after the holidays** The store increases the sale price by 20%. That means the new price is 36 + (20% of 36). 20% of 36 = 36 × 0.20 = 7.20. So, new price = 36 + 7.20 = 43.20. --- **Step 4: Conclusion** The final price after both changes is $43.20. --- **Note:** The final price is not $45 because a 20% decrease followed by a 20% increase on a different base amount does not return to the original price.

6. A local bookstore is having a clearance sale where all hardcover books are marked down by 40%. Noah finds a science encyclopedia originally priced at $75. At the checkout, he also gets an additional 10% discount for being a store member. What is the final price Noah pays for the encyclopedia after both discounts? Answer: $40.50 Solution: Calculate the first discount of 40% off the original price of $75. 40% of $75 = 0.40 × $75 = $30 Sale price after first discount = $75 - $30 = $45 Calculate the additional 10% member discount off the sale price of $45.
   Full step-by-step solution

   Step 1: Calculate the first discount of 40% off the original price of $75. 40% of $75 = 0.40 × $75 = $30 Sale price after first discount = $75 - $30 = $45 Step 2: Calculate the additional 10% member discount off the sale price of $45. 10% of $45 = 0.10 × $45 = $4.50 Final price after second discount = $45 - $4.50 = $40.50 The final price Noah pays is $40.50.

7. A $1200 laptop is discounted by 25% during a sale, then the sale price is increased by 8% for tax. What is the final price? Answer: $972 Solution: Calculate the 25% discount amount: 25% of $1200 = 0.25 × 1200 = $300 Calculate the sale price: $1200 - $300 = $900 Calculate the 8% tax amount: 8% of $900 = 0.08 × 900 = $72 Calculate the final price: $900 + $72 = $972 The final price is $972.
   Full step-by-step solution

   Step 1: Calculate the 25% discount amount: 25% of $1200 = 0.25 × 1200 = $300 Step 2: Calculate the sale price: $1200 - $300 = $900 Step 3: Calculate the 8% tax amount: 8% of $900 = 0.08 × 900 = $72 Step 4: Calculate the final price: $900 + $72 = $972 The final price is $972.

8. A $2000 smartphone 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 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 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.

9. Liam bought a rare comic book for $120. After one year, its value increased by 25%. The following year, its value decreased by 20% from the new price. What is the current value of Liam's comic book? Answer: 120 Solution: Liam bought the comic book for $120.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Initial price** Liam bought the comic book for $120. --- **Step 2: First year increase of 25%** A 25% increase means the new price is: Original price + 25% of original price = 120 + (25/100) * 120 = 120 + 0.25 * 120 = 120 + 30 = 150 So after one year, the value is $150. --- **Step 3: Second year decrease of 20%** Now the starting point is $150. A 20% decrease means the new price is: 150 - (20/100) * 150 = 150 - 0.20 * 150 = 150 - 30 = 120 --- **Step 4: Conclusion** The current value of the comic book is $120. --- **Final answer:** 120