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.

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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.