the price of a fan is first decreased by 28% and increased by 35%. if the resulting price is 1215, find the original price of the fan.

Let the original price of the fan be \( P \).

1. The price is first decreased by 28%. So, the price after this decrease is:
   \[
   P \times (1 - 0.28) = 0.72P
   \]

2. The price is then increased by 35%. So, the price after this increase becomes:
   \[
   0.72P \times (1 + 0.35) = 0.72P \times 1.35 = 0.972P
   \]

We are given that the final price is 1215. Therefore:
\[
0.972P = 1215
\]

Now, solve for \( P \):
\[
P = \frac{1215}{0.972} \approx 1250
\]

Thus, the original price of the fan is approximately \( \boxed{1250} \).

Would you like further clarification or a detailed breakdown?

Here are 5 related questions to explore further:
1. How would the calculation change if the price was decreased by 30% and then increased by 40%?
2. What would happen if the fan's price was first increased by 28% and then decreased by 35%?
3. How does compounding percentages affect prices compared to a single percentage adjustment?
4. Can you calculate the final price if the original price was 1250, but the percentage changes were reversed?
5. How would you solve this problem if the final price was unknown, but you had the percentage increases and decreases?

**Tip**: When dealing with percentage changes, always apply the percentage modifications in sequence and remember that a percentage decrease or increase is multiplicative, not additive.

The price of a fan is first decreased by 28% and increased by 35%. If the resulting price is 1215, find the original price of the fan.

Learn how to find the original price of a fan when its price is decreased by 28% and then increased by 35%, resulting in a final price of 1215. This problem covers percentage changes and linear algebraic equations, suitable for students in Grades 8-10.

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