Question

A merchant made a profit of 5 on the sale of a sweater that cost the merchant $15. What is the profit expressed as a percent of the merchant's cost? 
Give your answer to the nearest whole percent. 
 

Hint:

Be careful to identify what the percentage is based on. In this case, it's "percent of the merchant's cost," so the cost goes in the denominator. If it had asked for percent of the selling price, the selling price ($15 cost + $5 profit = $20) would have been the denominator.

Answer 1

Step 1: Understanding the Concept:
This problem asks to calculate the percent profit. Percent profit is the ratio of the profit to the original cost, expressed as a percentage.
Step 2: Key Formula or Approach:
The formula for percent profit relative to cost is:
\[ \text{Percent Profit} = \left(\frac{\text{Profit}}{\text{Cost}}\right) \times 100% \] Step 3: Detailed Explanation:
We are given:
- Profit = $5
- Cost = $15
Substitute these values into the formula:
\[ \text{Percent Profit} = \left(\frac{5}{15}\right) \times 100% \] First, simplify the fraction:
\[ \frac{5}{15} = \frac{1}{3} \] Now, calculate the percentage:
\[ \text{Percent Profit} = \frac{1}{3} \times 100% = 33.333...% \] The question asks for the answer to be rounded to the nearest whole percent.
\[ 33.333...% \approx 33% \] Step 4: Final Answer:
The profit expressed as a percent of the merchant's cost is 33%.