We can solve this problem by following these steps:

Step 1: Understanding the Problem

• The retailer wants to make a 40% profit on the selling price.
• A 30% discount will be applied on the selling price.
• The cost of the product to the retailer is $3.40.

Step 2: Setting up the Equation

Let the selling price before the discount be $S$.

After applying the discount, the price the customer pays is: $\text{Discounted price} = S - 30\% \times S = 0.70 \times S$

For the retailer to make a 40% profit on the selling price, the cost of the product ($3.40) should equal 60% of the selling price (since the profit is 40% of the selling price, 100% - 40% = 60%): $0.70S = 1.4 \times 3.40$

Step 3: Solving the Equation

We can now solve for $S$:

$0.70S = 1.4 \times 3.40 = 4.76$

Now divide both sides by 0.70: $S = \frac{4.76}{0.70} = 6.80$

Final Answer:

The product should be sold at $6.80 before applying the 30% discount.

Would you like more details on any part of this solution?

Here are 5 related questions:

1. How does the profit margin change with different discount rates?
2. What would the selling price be if the desired profit was 50% instead of 40%?
3. How would the selling price change if the discount were 20% instead of 30%?
4. What is the relationship between cost, selling price, and profit in percentage terms?
5. How do different discount strategies affect overall profitability?

Tip: Always work backward from the final price when considering discounts and profit margins.