if the price of a laptop is increased by 10% then decreased by 10%,will the final price be the same as the original price

To determine if the final price of a laptop will be the same as the original price after being increased by 10% and then decreased by 10%, we can follow these steps:

1. **Original Price**: Let the original price of the laptop be \( P \).

2. **Price after a 10% Increase**:
   \[
   P_{\text{increased}} = P + 0.10P = 1.10P
   \]

3. **Price after a 10% Decrease from the Increased Price**:
   \[
   P_{\text{final}} = P_{\text{increased}} - 0.10P_{\text{increased}} = 1.10P - 0.10(1.10P) = 1.10P - 0.11P = 0.99P
   \]

Thus, the final price of the laptop is \( 0.99P \), which is 99% of the original price \( P \). This indicates that the final price is actually less than the original price by 1%.

To conclude, the final price is not the same as the original price; it is 1% less than the original price.

Would you like any details or have any questions?

Here are 5 questions you might want to ask next:
1. How can I calculate the percentage change in a series of price changes?
2. Can you explain why the final price is less than the original price?
3. How do percentage increases and decreases affect each other?
4. What are some real-life applications of percentage change calculations?
5. How can I calculate compound percentage changes for multiple adjustments?

**Tip:** When dealing with percentage increases and decreases, remember that they do not cancel each other out exactly due to the change in the base value after each step.

Explore how a 10% increase followed by a 10% decrease affects the final price of a product. Learn the step-by-step calculation to determine if the final price matches the original price. This problem covers percentage change formulas and arithmetic operations, suitable for high school students.

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