Question

3.
An item costs $36. The price is increased by $15, then reduced by $15. Find the percent of increase and the percent of decrease.

Answer 1

Let's break down the problem step by step.

1. **Initial Cost:** The item initially costs $36.

2. **Price Increase:** The price is increased by $15.
\[
\text{New Price after Increase} = 36 + 15 = 51
\]

3. **Price Decrease:** The price is then reduced by $15.
\[
\text{New Price after Decrease} = 51 - 15 = 36
\]

Now, we need to calculate the percent increase and the percent decrease.

### Percent Increase:
The formula for percent increase is:
\[
\text{Percent Increase} = \left( \frac{\text{Increase}}{\text{Original Price}} \right) \times 100
\]
- Increase = New Price - Original Price = $51 - $36 = $15

Substituting the values:
\[
\text{Percent Increase} = \left( \frac{15}{36} \right) \times 100 \approx 41.67\%
\]

### Percent Decrease:
The formula for percent decrease is:
\[
\text{Percent Decrease} = \left( \frac{\text{Decrease}}{\text{New Price after Increase}} \right) \times 100
\]
- Decrease = New Price after Increase - Final Price = $51 - $36 = $15

Substituting the values:
\[
\text{Percent Decrease} = \left( \frac{15}{51} \right) \times 100 \approx 29.41\%
\]

### Summary
- **Percent Increase:** approximately **41.67%**
- **Percent Decrease:** approximately **29.41%**