• Percentage Increase: A rise in value expressed as a percentage of the original amount.
• Percentage Decrease: A reduction in value expressed as a percentage of the original amount.
• Original Amount: The initial value before any percentage change is applied.
• Final Amount: The value after a percentage increase or decrease has been applied.

1. Identify the Given Values: Determine whether the change is a percentage increase or decrease, and note the final amount.
2. Convert the Percentage Change: Express the percentage change as a decimal by dividing by 100.
3. Apply the Formula: Use the appropriate formula based on whether it's an increase or decrease.
4. Calculate the Original Amount: Perform the necessary arithmetic to find the initial value.

A shirt originally costs $50. After a 20% increase, the new price is $60. Find the original price.

Solution:

1. Final Amount (after increase) = $60
2. Percentage Increase = 20%
3. Original Amount = $\frac{60}{1 + \frac{20}{100}} = \frac{60}{1.2} = $50$

A laptop's price decreased by 15% to $850. Find the original price.

Solution:

1. Final Amount (after decrease) = $850
2. Percentage Decrease = 15%
3. Original Amount = $\frac{850}{1 - \frac{15}{100}} = \frac{850}{0.85} \approx $1000$

• Financial Planning: Determining the original investment before a rate of return.
• Sales and Discounts: Calculating the initial price before a discount was applied.
• Economics: Analyzing changes in economic indicators like GDP or inflation rates.
• Health and Fitness: Assessing original weight or measurements before changes.

• Mistaking Percentage Increase for Decrease: Always verify whether the problem involves an increase or decrease to apply the correct formula.
• Incorrect Conversion of Percentage: Ensure the percentage change is accurately converted to a decimal form.
• Misapplying the Formula: Carefully substitute values into the formula, paying attention to the "+" or "−" sign based on the scenario.
• Rounding Errors: Maintain precision during calculations to avoid inaccuracies in the final answer.

• Original Amount (Increase): $$\text{Original Amount} = \frac{\text{Final Amount}}{1 + \frac{\text{Percentage Increase}}{100}}$$
• Original Amount (Decrease): $$\text{Original Amount} = \frac{\text{Final Amount}}{1 - \frac{\text{Percentage Decrease}}{100}}$$

1. A jacket's price decreased by 25% to $150. What was the original price?

2. After a 10% increase, the population of a town is 5,500. What was the original population?

3. A car's value depreciated by 18% to $12,320. Find its original value.

4. The final score of a test increased by 5% to 210 points. What was the original score?

5. A restaurant's revenue decreased by 12% to $44,000. What was the original revenue?

Solution 1:

1. Final Amount = $150
2. Percentage Decrease = 25%
3. Original Amount = $\frac{150}{1 - \frac{25}{100}} = \frac{150}{0.75} = $200$

Solution 2:

1. Final Amount = 5,500
2. Percentage Increase = 10%
3. Original Population = $\frac{5500}{1 + \frac{10}{100}} = \frac{5500}{1.1} = 5000$

Solution 3:

1. Final Amount = $12,320
2. Percentage Decrease = 18%
3. Original Value = $\frac{12320}{1 - \frac{18}{100}} = \frac{12320}{0.82} = $15,000$

Solution 4:

1. Final Score = 210 points
2. Percentage Increase = 5%
3. Original Score = $\frac{210}{1 + \frac{5}{100}} = \frac{210}{1.05} = 200$ points

Solution 5:

1. Final Revenue = $44,000
2. Percentage Decrease = 12%
3. Original Revenue = $\frac{44000}{1 - \frac{12}{100}} = \frac{44000}{0.88} = $50,000$

• Reverse percentage problems involve finding the original amount before a percentage increase or decrease.
• Understanding the correct formula is crucial for accurate calculations.
• Applying this concept is essential in various real-life scenarios like finance, sales, and data analysis.
• A systematic approach helps avoid common mistakes and ensures precision.
• Mastery of reverse percentage problems enhances overall mathematical proficiency in the IB MYP curriculum.