Find the percent markup based on selling price, if the percent markup based on the cost is $$ 33 \% $$. (Round to the nearest tenth percent) Select one: a. $$ 55.0 \% $$ b. $$ 12.3 \% $$ c. $$ 25 \% $$ od. $$ 24.33 \% $$

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UpStudy AI · Accepted Answer

To determine the percent markup based on the selling price when the percent markup based on cost is $$ 33\% $$, follow these steps:

### Definitions:
- **Cost (C):** The original price of the item.
- **Selling Price (S):** The price at which the item is sold.
- **Percent Markup Based on Cost:** $$ \frac{S - C}{C} \times 100\% $$
- **Percent Markup Based on Selling Price:** $$ \frac{S - C}{S} \times 100\% $$

### Given:
- Percent markup based on cost: $$ 33\% $$
  
This means:
$$
\frac{S - C}{C} = 0.33 \quad \Rightarrow \quad S = 1.33C
$$

### Calculating Percent Markup Based on Selling Price:
$$
\frac{S - C}{S} = \frac{1.33C - C}{1.33C} = \frac{0.33C}{1.33C} = \frac{0.33}{1.33} \approx 0.2481 \quad \Rightarrow \quad 24.81\%
$$

### Rounding:
Rounding $$ 24.81\% $$ to the nearest tenth percent gives **24.8\%**.

### Selecting the Closest Option:
Among the given options:
- a. $$ 55.0\% $$
- b. $$ 12.3\% $$
- c. $$ 25\% $$
- d. $$ 24.33\% $$

**Option d. $$ 24.33\% $$** is the closest to our calculated value of $$ 24.8\% $$ and is the most accurate choice based on the provided options.

**Answer:**  
**d. $$ 24.33 \% $$**
The percent markup based on the selling price is approximately $$ 24.33\% $$.

Find the percent markup based on selling price, if the percent markup based on the cost is \( 33 \% \). (Round to the nearest tenth percent) Select one: a. \( 55.0 \% \) b. \( 12.3 \% \) c. \( 25 \% \) od. \( 24.33 \% \)

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