Percent Change

lessonbunny.com

Answer Key & Explanations

Percent Change · Grade 6 · Worksheet 2

1. Emma's school is planning a field trip to the science museum. The museum charges $12 per student, but offers a 15% discount for groups of 30 or more students. If 36 students are going on the field trip, how much will the school need to pay for all the student tickets after the discount? Answer: 367.20 Solution: 36 students × $12 per student = $432 15% of $432 = 0.15 × 432 = $64.80 $432 - $64.80 = $367.20 The school will need to pay $367.20 for all the student tickets after the discount.
   Full step-by-step solution

   Step 1: Calculate the original cost for all students 36 students × $12 per student = $432 Step 2: Calculate the discount amount 15% of $432 = 0.15 × 432 = $64.80 Step 3: Subtract the discount from the original cost $432 - $64.80 = $367.20 The school will need to pay $367.20 for all the student tickets after the discount.

2. Emma's favorite bookstore is having a clearance sale. A novel originally priced at $28 is marked down by 25%. After the sale ends, the bookstore increases the clearance price by 30% for the regular inventory. What is the final price of the novel after both the discount and the price increase? Answer: $27.30 Solution: Original price: $28 Discount: 25% of $28 = 0.25 × 28 = $7 Sale price = Original price - Discount = $28 - $7 = $21 Price increase: 30% of $21 = 0.30 × 21 = $6.30 Final price = Sale price + Increase = $21 + $6.30 = $27.30 The final price of the novel is $27.30.
   Full step-by-step solution

   Step 1: Calculate the discount amount Original price: $28 Discount: 25% of $28 = 0.25 × 28 = $7 Step 2: Calculate the sale price Sale price = Original price - Discount = $28 - $7 = $21 Step 3: Calculate the price increase after sale Price increase: 30% of $21 = 0.30 × 21 = $6.30 Step 4: Calculate the final price Final price = Sale price + Increase = $21 + $6.30 = $27.30 The final price of the novel is $27.30.

3. Noah's electronics store is having a clearance sale on tablets. A popular model originally priced at $1,200 is marked down by 25%. After two weeks, the store applies an additional 15% discount to the remaining tablets. What is the final price of the tablet after both discounts? Answer: $765 Solution: Calculate the first discount of 25% off $1,200 25% of $1,200 = 0.25 × 1,200 = $300 Price after first discount = $1,200 - $300 = $900 Calculate the second discount of 15% off the new price of $900 15% of $900 = 0.15 × 900 = $135 Price after second discount = $900 - $135 = $765 The final price of…
   Full step-by-step solution

   Step 1: Calculate the first discount of 25% off $1,200 25% of $1,200 = 0.25 × 1,200 = $300 Price after first discount = $1,200 - $300 = $900 Step 2: Calculate the second discount of 15% off the new price of $900 15% of $900 = 0.15 × 900 = $135 Price after second discount = $900 - $135 = $765 The final price of the tablet after both discounts is $765.

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

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

5. Liam's favorite video game originally cost $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 these changes? Answer: 43.2 Solution: The original price is $45. 80% as a decimal is 0.80. So, sale price after discount = 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 after discount = 45 × 0.80. Calculation: 45 × 0.80 = 36. So after the holiday sale, the price is $36. --- **Step 3: Apply the 20% increase after the holidays** The store increases the sale price by 20%. A 20% increase means multiply by 1.20. So, new price = 36 × 1.20. Calculation: 36 × 1.20 = 43.2. --- **Step 4: Conclusion** The final price after the discount and then the increase is $43.20. --- **Final Answer:** 43.2

6. Noah invested $2,500 in a savings account that earned 4% interest in the first year. In the second year, the interest rate increased to 5%. How much money did Noah have in his account at the end of the second year? Answer: 2730 Solution: Calculate the first year's interest: 4% of $2,500 = 0.04 × 2500 = $100 Calculate the balance after first year: $2,500 + $100 = $2,600 Calculate the second year's interest: 5% of $2,600 = 0.05 × 2600 = $130 Calculate the final balance: $2,600 + $130 = $2,730 Noah had $2,730 in his account at the…
   Full step-by-step solution

   Step 1: Calculate the first year's interest: 4% of $2,500 = 0.04 × 2500 = $100 Step 2: Calculate the balance after first year: $2,500 + $100 = $2,600 Step 3: Calculate the second year's interest: 5% of $2,600 = 0.05 × 2600 = $130 Step 4: Calculate the final balance: $2,600 + $130 = $2,730 Noah had $2,730 in his account at the end of the second year.

7. A $1500 computer is discounted by 20% during a sale, then the sale price is increased by 12% for a restocking fee. What is the final price? Answer: $1344 Solution: Calculate the 20% discount on $1500 20% of $1500 = 0.20 × 1500 = $300 Discounted price = $1500 - $300 = $1200 Calculate the 12% increase on the discounted price 12% of $1200 = 0.12 × 1200 = $144 Final price = $1200 + $144 = $1344 The final price is $1344.
   Full step-by-step solution

   Step 1: Calculate the 20% discount on $1500 20% of $1500 = 0.20 × 1500 = $300 Discounted price = $1500 - $300 = $1200 Step 2: Calculate the 12% increase on the discounted price 12% of $1200 = 0.12 × 1200 = $144 Final price = $1200 + $144 = $1344 The final price is $1344.

8. A $1200 laptop is discounted by 25% during a sale, then the sale price is increased by 8% for sales 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 answer 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 answer is $972.