Instructions
This worksheet focuses on calculating percentage increases and decreases. These skills are essential for budgeting, understanding discounts, and analyzing financial data.
Key Methods:
- To calculate a percentage increase: Convert the percentage to a decimal, add 1, and multiply the original amount by this new number (the multiplier). Example: Increase by 20% -> Multiplier is 1 + 0.20 = 1.20
- To calculate a percentage decrease: Convert the percentage to a decimal, subtract it from 1, and multiply the original amount by this new number (the multiplier). Example: Decrease by 15% -> Multiplier is 1 - 0.15 = 0.85
Complete all sections, showing your calculation steps when asked.
Section 1: Finding the New Value (Direct Calculation)
Calculate the final amount for each scenario using the multiplier method.
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Increase $400 by 10%. Calculation: Final Amount: $
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Decrease $150 by 20%. Calculation: Final Amount: $
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Increase $60 by 5%. Calculation: Final Amount: $
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Decrease $900 by 30%. Calculation: Final Amount: $
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A company wants to increase its production of video games from 8,000 units to 8,000 units plus 12.5%. How many units will they produce? Calculation: Final Units:
Section 2: Real-World Shopping Scenarios
Complete the following table tracking sales and price changes in a local store. Write the calculation/multiplier used in the third column.
| Original Price | % Change | Calculation / Multiplier Used | Final Price |
|---|---|---|---|
| $50.00 | 25% Increase (Markup) | $50.00 \times 1.25$ | $62.50 |
| $120.00 | 15% Decrease (Discount) | ||
| $8.00 | 50% Increase (Tax/Cost) | ||
| $350.00 | 10% Decrease (Sale) | ||
| $1,500.00 | 2% Increase (Inflation) | ||
| $75.00 | 33% Decrease (Clearance) |
Reflection Prompt:
If a store offers a 20% discount on a $100 shirt, and then offers an additional 10% off the discounted price, will the total savings be 30%? Explain why or why not.
Explanation:
Section 3: The Challenge (Finding the Original Amount)
In some real-world situations, you know the final price and the percentage change, but you need to find the original price. This requires the inverse operation (division).
Hint: If the final price is $198 after a 10% increase, you must divide $198 by the multiplier (1.10) to find the original price.
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A used laptop is sold for $480. This price represents a 20% depreciation (decrease) from its original cost. What was the original cost of the laptop?
Step 1: Determine the multiplier. (1 - 0.20 = 0.80) Step 2: Divide the final price by the multiplier.
Calculation: Original Cost: $
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(Advanced Challenge) After a 5% sales tax was added, Maria paid a total of $336 for a bicycle. What was the price of the bicycle before the tax?
Calculation: Original Price (before tax): $
Answer Key
Section 1: Finding the New Value (Direct Calculation)
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Increase $400 by 10%. Calculation: $400 \times 1.10$ Final Amount: $440.00
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Decrease $150 by 20%. Calculation: $150 \times 0.80$ Final Amount: $120.00
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Increase $60 by 5%. Calculation: $60 \times 1.05$ Final Amount: $63.00
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Decrease $900 by 30%. Calculation: $900 \times 0.70$ Final Amount: $630.00
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A company wants to increase its production of video games from 8,000 units to 8,000 units plus 12.5%. How many units will they produce? Calculation: $8,000 \times 1.125$ Final Units: 9,000 units
Section 2: Real-World Shopping Scenarios
| Original Price | % Change | Calculation / Multiplier Used | Final Price |
|---|---|---|---|
| $50.00 | 25% Increase (Markup) | $50.00 \times 1.25$ | $62.50 |
| $120.00 | 15% Decrease (Discount) | $120.00 \times 0.85$ | $102.00 |
| $8.00 | 50% Increase (Tax/Cost) | $8.00 \times 1.50$ | $12.00 |
| $350.00 | 10% Decrease (Sale) | $350.00 \times 0.90$ | $315.00 |
| $1,500.00 | 2% Increase (Inflation) | $1,500.00 \times 1.02$ | $1,530.00 |
| $75.00 | 33% Decrease (Clearance) | $75.00 \times 0.67$ | $50.25 |
Reflection Prompt Answer:
No, the total savings will not be 30%. The second discount (10%) is calculated on the already reduced price, not the original price. 20% off $100 = $80. 10% off $80 = $8 discount. ($80 - $8 = $72). Total savings: $100 - $72 = $28 (which is 28%).
Section 3: The Challenge (Finding the Original Amount)
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A used laptop is sold for $480. This price represents a 20% depreciation (decrease) from its original cost. What was the original cost of the laptop?
Calculation: $480 / 0.80$ Original Cost: $600.00
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(Advanced Challenge) After a 5% sales tax was added, Maria paid a total of $336 for a bicycle. What was the price of the bicycle before the tax?
Calculation: $336 / 1.05$ Original Price (before tax): $320.00