Question
If the markup on a flourescent ight fixture is \( 120 \% \) based on cost, what is corresponding percent markup based on selling price?
Ask by Parry Page. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
A markup of approximately 54.55% based on the selling price.
Solution
To determine the corresponding percent markup based on the selling price when the markup on cost is \( 120\% \), follow these steps:
1. **Define the Variables:**
- Let \( C \) be the **cost** of the fluorescent light fixture.
- Let \( S \) be the **selling price**.
2. **Markup Based on Cost:**
\[
\text{Markup on Cost} = \frac{S - C}{C} \times 100\% = 120\%
\]
This implies:
\[
\frac{S - C}{C} = 1.20 \quad \Rightarrow \quad S = 2.20C
\]
3. **Markup Based on Selling Price:**
\[
\text{Markup on Selling Price} = \frac{S - C}{S} \times 100\%
\]
Substitute \( S = 2.20C \):
\[
\frac{2.20C - C}{2.20C} = \frac{1.20C}{2.20C} = \frac{1.20}{2.20} = \frac{12}{22} = \frac{6}{11} \approx 0.5454
\]
Convert to percentage:
\[
0.5454 \times 100\% \approx 54.55\%
\]
**Final Answer:**
A markup of approximately 54.55 % based on the selling price.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find the percent markup based on the selling price, we can start by expressing the markup in terms of cost. If the cost of the fluorescent light fixture is \( C \), the selling price \( S \) will be: \[ S = C + 1.2C = 2.2C \] The markup based on selling price is then calculated as: \[ \text{Percent Markup} = \frac{S - C}{S} \times 100 \] Substituting \( S \): \[ \text{Percent Markup} = \frac{2.2C - C}{2.2C} \times 100 = \frac{1.2C}{2.2C} \times 100 \approx 54.55\% \] So, the corresponding percent markup based on the selling price is approximately \( 54.55\% \).
