how can you find the original amount in real-world percent problems?
To find the original amount in real-world percent problems, you can use the formula:
Original Amount = [100% / (100% + Percent)] × Final Amount
Here's an example to illustrate the process:
Problem: A shirt is on sale for 20% off. The final price of the shirt is $40. What was the original price?
Solution:
1. Identify the information given:
- Percent off: 20%
- Final price: $40
2. Apply the formula:
Original Amount = [100% / (100% + Percent)] × Final Amount
Insert the values:
Original Amount = [100% / (100% + 20%)] × $40
3. Simplify the expression inside the brackets:
Original Amount = [100% / (100% + 0.20)] × $40
4. Calculate the denominator:
100% + 20% = 120%
5. Convert 120% to decimal form:
120% = 120/100 = 1.2
6. Substitute the values and calculate:
Original Amount = [100% / 1.2] × $40
Original Amount = (100/1.2) × $40
Original Amount = (83.33) × $40
Original Amount ≈ $333.33
Therefore, the original price of the shirt was approximately $333.33.