Workwear Station uses a markup on cost of 60% to establish its retail prices. This pricing rule builds in a profit of 22% of cost. What rate of markdown can Workwear Station offer and just break even on the reduced price? (Round your answer to 1 decimal place.)

Rate of markdown 

We are tasked with finding the rate of markdown Workwear Station can offer and still break even on the reduced price, given that they use a 60% markup on cost and aim to achieve a profit of 22% of cost. Let's break this problem into steps.

### Step 1: Understanding the relationship between markup and profit

- **Markup on cost**: 60%
  - This means the selling price $ P_s $ is 160% of the cost $ C $ because the price includes both the cost and the markup. Hence, $ P_s = 1.60C $.
  
- **Profit as a percentage of cost**: 22%
  - This means Workwear Station needs to ensure that their selling price includes a 22% profit on the cost. Therefore, to just break even after the markdown, they want to sell at exactly their cost, i.e., $ P_s = C $.

### Step 2: Defining the selling price after the markdown

The markdown rate is the percentage by which the selling price can be reduced so that Workwear Station breaks even. The break-even price equals the original cost $ C $.

Let the rate of markdown be $ x $. Then, the selling price after the markdown $ P_m $ will be:
\[
P_m = P_s \times (1 - x)
\]

At break-even, the price after the markdown should equal the cost:
\[
P_m = C
\]

Substituting $ P_s = 1.60C $ into this equation:
\[
C = 1.60C \times (1 - x)
\]

### Step 3: Solving for the markdown rate

Now we solve for $ x $:
\[
C = 1.60C \times (1 - x)
\]

Divide both sides by $ C $ (since $ C \neq 0 $):
\[
1 = 1.60 \times (1 - x)
\]

Solve for $ 1 - x $:
\[
1 - x = \frac{1}{1.60}
\]
\[
1 - x = 0.625
\]

Finally, solve for $ x $:
\[
x = 1 - 0.625 = 0.375
\]

### Step 4: Conclusion

The markdown rate is $ 0.375 $, or 37.5%. Therefore, Workwear Station can offer a markdown of **37.5%** and just break even.

---

Would you like further details or explanations?

Here are 5 related questions to explore:
1. How does markup differ from margin in pricing strategies?
2. What would be the selling price if the cost were $100 and the markup was 60%?
3. If Workwear Station wanted a profit of 30%, what markdown rate would still allow it to break even?
4. How does markdown affect profitability in the long run?
5. What is the difference between a percentage markup on cost and a percentage discount from the selling price?

**Tip:** Understanding the distinction between markup on cost and profit margin is essential for accurate pricing strategies.

Workwear Station uses a markup on cost of 60% to establish its retail prices. This pricing rule builds in a profit of 22% of cost. What rate of markdown can Workwear Station offer and just break even on the reduced price? (Round your answer to 1 decimal place.)

Find out how to calculate the rate of markdown Workwear Station can offer to break even, given a 60% markup and 22% profit margin. This step-by-step solution explains the concepts of markup, markdown, and break-even pricing, suitable for high school students in Grades 9-12.

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