Percent Change

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Answer Key & Explanations

Percent Change · Grade 6 · Worksheet 3

1. Emma's favorite clothing store is having a clearance sale. A jacket originally priced at $120 is marked down by 30%. Then, an additional 15% discount is applied at the register for store cardholders. What is the final price Emma pays for the jacket? Answer: 71.40 Solution: Calculate the first discount of 30% off $120 30% of $120 = 0.30 × 120 = $36 Sale price after first discount = $120 - $36 = $84 Calculate the additional 15% discount off $84 15% of $84 = 0.15 × 84 = $12.60 Final price after second discount = $84 - $12.60 = $71.40 The answer is $71.40.
   Full step-by-step solution

   Step 1: Calculate the first discount of 30% off $120 30% of $120 = 0.30 × 120 = $36 Sale price after first discount = $120 - $36 = $84 Step 2: Calculate the additional 15% discount off $84 15% of $84 = 0.15 × 84 = $12.60 Final price after second discount = $84 - $12.60 = $71.40 The answer is $71.40.

2. Tane is training for a cross-country race. In the first week, he ran a total of 3,125 meters. In the second week, he increased his total distance by 12%. In the third week, he decreased his distance from the second week by 8%. What is the total distance Tane ran in the third week? Answer: 3,220 meters Solution: Find the distance after the 12% increase in week 2. 12% of 3,125 = 0.12 × 3,125 = 375 Week 2 distance = 3,125 + 375 = 3,500 meters Find the distance after the 8% decrease from week 2 in week 3.
   Full step-by-step solution

   Step 1: Find the distance after the 12% increase in week 2. 12% of 3,125 = 0.12 × 3,125 = 375 Week 2 distance = 3,125 + 375 = 3,500 meters Step 2: Find the distance after the 8% decrease from week 2 in week 3. 8% of 3,500 = 0.08 × 3,500 = 280 Week 3 distance = 3,500 - 280 = 3,220 meters The total distance Tane ran in the third week is 3,220 meters.

3. 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.

4. A rectangular vegetable plot is drawn on a coordinate grid with corners at (3, 4), (15, 4), (15, 10), and (3, 10). Noah wants to increase the area of the plot by 80% by extending only the longer sides outward equally in both directions. What will be the new x-coordinates of the left and right corners after the extension? Answer: Left: -0.6, Right: 18.6 Solution: Find original dimensions. Horizontal length: 15 - 3 = 12 units Vertical length: 10 - 4 = 6 units The longer sides are the horizontal sides (12 > 6). Original area.
   Full step-by-step solution

   Step 1: Find original dimensions. Horizontal length: 15 - 3 = 12 units Vertical length: 10 - 4 = 6 units The longer sides are the horizontal sides (12 > 6). Step 2: Original area. Area = 12 × 6 = 72 square units Step 3: Target area after 80% increase. Increase = 80% of 72 = 0.8 × 72 = 57.6 Target area = 72 + 57.6 = 129.6 square units Step 4: New horizontal length. Since vertical stays 6, new horizontal length = 129.6 ÷ 6 = 21.6 units Step 5: Extension amount. Increase in length = 21.6 - 12 = 9.6 units Extension on each side = 9.6 ÷ 2 = 4.8 units Step 6: New x-coordinates. Left side originally at x = 3 moves left: 3 - 4.8 = -1.8 Right side originally at x = 15 moves right: 15 + 4.8 = 19.8 The new x-coordinates are -1.8 and 19.8. The answer is Left: -1.8, Right: 19.8.

5. A smartphone originally costs $1200. During a holiday sale, the price is reduced by 15%. After the sale, the price is increased by 15% of the sale price to return to the regular price. What is the final price of the smartphone after the increase? Round your answer to the nearest cent. Answer: 1173.00 Solution: Original price = $1200 Apply the 15% discount Discount amount = 15% of 1200 Discount amount = 0.15 × 1200 = 180 Sale price = Original price − Discount Sale price = 1200 − 180 = 1020 Apply the 15% increase on the sale price Increase amount = 15% of 1020 Increase amount = 0.15 × 1020 = 153 Final…
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Original price** Original price = $1200 --- **Step 2: Apply the 15% discount** Discount amount = 15% of 1200 Discount amount = 0.15 × 1200 = 180 Sale price = Original price − Discount Sale price = 1200 − 180 = 1020 --- **Step 3: Apply the 15% increase on the sale price** Increase amount = 15% of 1020 Increase amount = 0.15 × 1020 = 153 --- **Step 4: Add the increase to the sale price** Final price = Sale price + Increase Final price = 1020 + 153 = 1173 --- **Step 5: Round to nearest cent** 1173.00 is already to the nearest cent. --- **Final Answer:** 1173.00

6. Emma's bicycle was valued at $1500. After a year, its value decreased by 15%. What is the new value of the bicycle? Answer: 1275 Solution: Find the amount of decrease: 15% of $1500 = 0.15 × 1500 = $225. Subtract the decrease from the original value: $1500 - $225 = $1275. The new value of the bicycle is $1275.
   Full step-by-step solution

   Step 1: Find the amount of decrease: 15% of $1500 = 0.15 × 1500 = $225. Step 2: Subtract the decrease from the original value: $1500 - $225 = $1275. The new value of the bicycle is $1275.

7. A smartphone originally costs $1,250. During a holiday sale, the price is decreased by 24%. What is the final sale price of the smartphone? Answer: 950 Solution: The original price is $1,250. The price is decreased by 24%. That means we pay 100% - 24% = 76% of the original price.
   Full step-by-step solution

   Step 1: Understand the problem. The original price is $1,250. The price is decreased by 24%. That means we pay 100% - 24% = 76% of the original price. Step 2: Convert 76% to a decimal. 76% = 76 / 100 = 0.76 Step 3: Multiply the original price by the decimal. Final price = 1250 × 0.76 Step 4: Perform the multiplication. First, 1250 × 0.76 = 1250 × (76 / 100) 1250 × 76 = 1250 × 70 + 1250 × 6 1250 × 70 = 87500 1250 × 6 = 7500 87500 + 7500 = 95000 Step 5: Divide by 100. 95000 / 100 = 950 Step 6: State the final answer. The sale price after a 24% discount is $950.

8. Olivia is tracking the value of her vintage guitar collection. She bought a rare acoustic guitar for $1,500. After one year, the value of the guitar increased by 20%. The following year, the value decreased by 15% from the new value. What is the current value of Olivia's guitar after these two years? Answer: 1530 Solution: Calculate the value after the 20% increase. Original value: $1,500 20% of $1,500 = 0.20 x 1,500 = $300 Value after increase: $1,500 + $300 = $1,800 Calculate the 15% decrease from the new value.
   Full step-by-step solution

   Step 1: Calculate the value after the 20% increase. Original value: $1,500 20% of $1,500 = 0.20 x 1,500 = $300 Value after increase: $1,500 + $300 = $1,800 Step 2: Calculate the 15% decrease from the new value. Value after increase: $1,800 15% of $1,800 = 0.15 x 1,800 = $270 Value after decrease: $1,800 - $270 = $1,530 The current value of Olivia's guitar is $1,530.