Percent Change

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Answer Key & Explanations

Percent Change · Grade 6 · Worksheet 1

1. 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.

2. Mere is looking at a rectangular vegetable garden drawn on a coordinate plane. The garden has corners at (2, 2), (14, 2), (14, 8), and (2, 8). She wants to decrease the garden's area by 30% by reducing only the longer sides inward equally from both directions. What will be the new x-coordinates of the corners that were originally at (2, 2) and (2, 8)? Answer: 3.8 and 12.2 Solution: Find the original dimensions. Horizontal side (length): 14 - 2 = 12 units Vertical side (width): 8 - 2 = 6 units The longer sides are horizontal (12 units). Calculate the original area.
   Full step-by-step solution

   Step 1: Find the original dimensions. Horizontal side (length): 14 - 2 = 12 units Vertical side (width): 8 - 2 = 6 units The longer sides are horizontal (12 units). Step 2: Calculate the original area. Area = 12 × 6 = 72 square units Step 3: Calculate the new area after a 30% decrease. 30% decrease means the new area is 70% of the original. New area = 72 × 0.7 = 50.4 square units Step 4: Find the new horizontal dimension. The vertical dimension stays at 6 units. New horizontal dimension = new area ÷ width = 50.4 ÷ 6 = 8.4 units Step 5: Calculate the total reduction in the horizontal dimension. Original horizontal dimension = 12 units New horizontal dimension = 8.4 units Total reduction = 12 - 8.4 = 3.6 units Step 6: Since the reduction is equal on both sides, each side moves inward by half the reduction. Movement inward = 3.6 ÷ 2 = 1.8 units Step 7: Find the new x-coordinates. Original left x-coordinate = 2, moves right by 1.8: 2 + 1.8 = 3.8 Original right x-coordinate = 14, moves left by 1.8: 14 - 1.8 = 12.2 The new x-coordinates are 3.8 and 12.2.

3. A tech company's stock was valued at $1,250 per share at the beginning of the year. During the first quarter, the stock price increased by 18%. In the second quarter, the price decreased by 12% from the new value. What is the stock price per share after both quarterly changes? Answer: $1298 Solution: Calculate the stock price after the 18% increase in the first quarter.
   Full step-by-step solution

   Step 1: Calculate the stock price after the 18% increase in the first quarter. 18% of $1,250 = 0.18 × 1,250 = $225 New price after increase = $1,250 + $225 = $1,475 Step 2: Calculate the stock price after the 12% decrease in the second quarter. 12% of $1,475 = 0.12 × 1,475 = $177 New price after decrease = $1,475 - $177 = $1,298 The final stock price per share after both quarterly changes is $1,298.

4. A $1500 computer is discounted by 20%, then the sale price is increased by 10%. What is the final price? Answer: $1320 Solution: Calculate the 20% discount on $1500 20% of $1500 = 0.20 × 1500 = $300 $1500 - $300 = $1200 Calculate the 10% increase on the sale price 10% of $1200 = 0.10 × 1200 = $120 $1200 + $120 = $1320 The final price is $1320.
   Full step-by-step solution

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

5. Mason is tracking the value of his vintage video game collection. Last year, the collection was valued at $1,600. This year, after adding a rare game, the collection is now worth $2,080. What is the percent increase in the value of Mason's collection? Answer: 30% Solution: Find the increase in value: $2,080 - $1,600 = $480 Divide the increase by the original value: $480 / $1,600 = 0.3 Convert to a percentage: 0.3 x 100 = 30% The percent increase in the value of Mason's collection is 30%.
   Full step-by-step solution

   Step 1: Find the increase in value: $2,080 - $1,600 = $480 Step 2: Divide the increase by the original value: $480 / $1,600 = 0.3 Step 3: Convert to a percentage: 0.3 x 100 = 30% The percent increase in the value of Mason's collection is 30%.

6. A rectangular swimming pool is drawn on a coordinate plane with corners at (1, 2), (11, 2), (11, 7), and (1, 7). The pool owner wants to increase the pool's area by 40% by extending only the longer sides outward equally in both directions. What will be the new coordinates of the corners that move during this transformation? Answer: (0, 2), (12, 2), (12, 7), (0, 7) Solution: Calculate the current dimensions of the pool. Horizontal side: 11 - 1 = 10 units Vertical side: 7 - 2 = 5 units Calculate the current area.
   Full step-by-step solution

   Step 1: Calculate the current dimensions of the pool. Horizontal side: 11 - 1 = 10 units Vertical side: 7 - 2 = 5 units Step 2: Calculate the current area. Area = length × width = 10 × 5 = 50 square units Step 3: Calculate the target area after 40% increase. 40% of 50 = 0.4 × 50 = 20 Target area = 50 + 20 = 70 square units Step 4: Since only the longer sides are extended, the width remains 5 units. Let the new length be L. L × 5 = 70 L = 70 ÷ 5 = 14 units Step 5: Calculate how much the length increases. Original length: 10 units New length: 14 units Increase = 14 - 10 = 4 units Step 6: Since the extension is equal in both directions, each side moves outward by half the increase. 4 ÷ 2 = 2 units Step 7: Determine the new coordinates. Original left side at x = 1 moves left by 2 units: 1 - 2 = -1 Original right side at x = 11 moves right by 2 units: 11 + 2 = 13 Vertical coordinates remain unchanged at y = 2 and y = 7 Step 8: Write the new coordinates. Bottom-left: (-1, 2) Bottom-right: (13, 2) Top-right: (13, 7) Top-left: (-1, 7) The answer is (-1, 2), (13, 2), (13, 7), (-1, 7).

7. Hana is training for a charity run. In her first week, she ran a total of 1,200 meters. In the second week, she increased her distance and ran a total of 1,500 meters. What is the percent increase in the distance Hana ran from the first week to the second week? Answer: 25% Solution: Find the increase in distance. New distance: 1,500 meters. Original distance: 1,200 meters.
   Full step-by-step solution

   Step 1: Find the increase in distance. New distance: 1,500 meters. Original distance: 1,200 meters. Increase = 1,500 - 1,200 = 300 meters. Step 2: Divide the increase by the original value: 300 / 1,200 = 0.25. Step 3: Multiply by 100 to convert to a percentage: 0.25 x 100 = 25%. The percent increase is 25%.

8. A $1200 laptop is discounted by 25%, 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 Subtract the discount from the original price: $1200 - $300 = $900 Calculate the 8% tax amount on the sale price: 8% of $900 = 0.08 × 900 = $72 Add the tax to the sale 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: Subtract the discount from the original price: $1200 - $300 = $900 Step 3: Calculate the 8% tax amount on the sale price: 8% of $900 = 0.08 × 900 = $72 Step 4: Add the tax to the sale price: $900 + $72 = $972 The final price is $972.