: If the price of a product is first decreased by 15% and then increased by 12%, then what is the percentage change in the price?

To find the percentage change in the price of a product that is first decreased by 15% and then increased by 12%, we can follow these steps:

1. Let the original price be \( P \).
2. The price after a 15% decrease:
   \[
   P_{\text{new1}} = P \times (1 - 0.15) = 0.85P
   \]
3. The price after a 12% increase on the new price:
   \[
   P_{\text{new2}} = 0.85P \times (1 + 0.12) = 0.85P \times 1.12
   \]
4. Simplifying this:
   \[
   P_{\text{new2}} = 0.85 \times 1.12 \times P = 0.952P
   \]
5. The final price is 0.952 times the original price \( P \).

To find the overall percentage change:
\[
\text{Percentage Change} = \left(\frac{P_{\text{new2}} - P}{P}\right) \times 100
\]
\[
= \left(\frac{0.952P - P}{P}\right) \times 100
\]
\[
= (0.952 - 1) \times 100
\]
\[
= -0.048 \times 100


Learn how to calculate the percentage change in price when it is first decreased by 15% and then increased by 12%. This problem involves basic percentage calculations and is suitable for Grades 7-9.

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