The cost of product to a retailer is $3.40, If the retailer wishes to make a profit of 40% on the selling price after the product discount 30%. At what price should the product be sold?

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.

The cost of a product to a retailer is $3.40. If the retailer wishes to make a profit of 40% on the selling price after the product discount of 30%, at what price should the product be sold?

Learn how to determine the selling price of a product that costs $3.40, where the retailer wants to make a 40% profit after applying a 30% discount. This step-by-step guide covers key concepts in algebra, percentages, and profit calculation. Suitable for students in Grades 8-10.

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