3.

Question

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%