Percent Change

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Answer Key & Explanations

Percent Change · Grade 6 · Worksheet 2

1. Emma's school is planning a field trip and needs to raise $1,200. They have currently raised $480 through bake sales. What percentage of their fundraising goal have they reached so far? Answer: 40% Solution: Identify the part collected and the total goal. Part collected = $480 Total goal = $1,200 Calculate the fraction of the goal that has been reached. Fraction = Part / Total = 480 / 1200 Simplify the fraction.
   Full step-by-step solution

   Step 1: Identify the part collected and the total goal. Part collected = $480 Total goal = $1,200 Step 2: Calculate the fraction of the goal that has been reached. Fraction = Part / Total = 480 / 1200 Step 3: Simplify the fraction. 480 / 1200 = 48 / 120 = 4 / 10 = 2 / 5 Step 4: Convert the fraction to a percentage. Percentage = (Part / Total) × 100% Percentage = (480 / 1200) × 100% Step 5: Perform the calculation. (480 / 1200) = 0.4 0.4 × 100% = 40% The school has reached 40% of their fundraising goal.

2. A rectangular garden measures 12 meters by 8 meters. The owner wants to increase the garden's area by 50% by extending both dimensions equally. What will be the new length of the longer side after this proportional increase? Answer: 14.7 Solution: Find the current area of the garden. Current length = 12 m Current width = 8 m Current area = length × width = 12 × 8 = 96 m² Determine the desired new area after a 50% increase.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Find the current area of the garden.** Current length = 12 m Current width = 8 m Current area = length × width = 12 × 8 = 96 m² --- **Step 2: Determine the desired new area after a 50% increase.** A 50% increase means multiply the current area by 1.5. New area = 96 × 1.5 = 144 m² --- **Step 3: Set up the proportional increase.** Let the increase factor be \( k \) (same for both length and width). New length = 12k New width = 8k New area = (12k) × (8k) = 96k² --- **Step 4: Solve for \( k \).** We know new area = 144, so: 96k² = 144 k² = 144 / 96 k² = 1.5 k = √1.5 --- **Step 5: Compute \( k \).** √1.5 = √(3/2) = √3 / √2 ≈ 1.7320508 / 1.41421356 ≈ 1.22474487 --- **Step 6: Find the new length of the longer side.** Longer side originally = 12 m New longer side = 12 × k ≈ 12 × 1.22474487 ≈ 14.6969384 --- **Step 7: Round to one decimal place (as in the given answer).** 14.6969... → 14.7 --- **Final answer:** 14.7

3. 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.

4. 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.

5. A technology 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's price per share after both quarterly changes? Answer: $1298 Solution: Original price: $1,250 18% increase = 1,250 × 0.18 = $225 New price after first quarter = 1,250 + 225 = $1,475 Price after first quarter: $1,475 12% decrease = 1,475 × 0.12 = $177 New price after second quarter = 1,475 - 177 = $1,298 The final stock price is $1,298 per share.
   Full step-by-step solution

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

6. A $3200 camera is discounted by 30% during a sale, then the sale price is increased by 12% for a restocking fee. What is the final price? Answer: 2508.8 Solution: Calculate the discount amount: 30% of $3200 = 0.30 × 3200 = $960. Discounted price = $3200 - $960 = $2240. Calculate the restocking fee: 12% of $2240 = 0.12 × 2240 = $268.80.
   Full step-by-step solution

   Step 1: Calculate the discount amount: 30% of $3200 = 0.30 × 3200 = $960. Discounted price = $3200 - $960 = $2240. Step 2: Calculate the restocking fee: 12% of $2240 = 0.12 × 2240 = $268.80. Final price = $2240 + $268.80 = $2508.80. The answer is $2508.80.

7. Ava is tracking the price of her favorite video game console. The console originally cost $1,160. After a holiday sale, the price dropped to $986. What is the percent decrease in the price of the console? Answer: 15% Solution: Find the amount of the decrease. Original price: $1,160 New price: $986 Decrease = $1,160 - $986 = $174 Divide the decrease by the original price. $174 ÷ $1,160 = 0.15 Convert the decimal to a percentage.
   Full step-by-step solution

   Step 1: Find the amount of the decrease. Original price: $1,160 New price: $986 Decrease = $1,160 - $986 = $174 Step 2: Divide the decrease by the original price. $174 ÷ $1,160 = 0.15 Step 3: Convert the decimal to a percentage. 0.15 × 100 = 15% The percent decrease in the price of the console is 15%.