How much should a food manufacturer sell pound of canned meat if his cost is P30 per can and he wants to make a 20% profit on the selling price for after giving away an 8% discount

To determine the selling price of the canned meat, let's break down the problem step by step:

### 1. Define the Variables:
- Let \( S \) be the selling price before discount.
- The cost per can \( C \) is \( \text{P}30 \).
- Desired profit margin is 20% on the selling price.
- Discount given is 8%.

### 2. Set up the Equation:

The manufacturer wants to make a 20% profit on the selling price after giving an 8% discount. Therefore, the price after discount, \( S_{\text{after discount}} \), can be written as:
\[
S_{\text{after discount}} = S \times (1 - 0.08) = S \times 0.92
\]

To achieve a 20% profit on the cost, the price after discount should be:
\[
S_{\text{after discount}} = \text{Cost} \times (1 + 0.20) = 30 \times 1.20 = \text{P}36
\]

### 3. Solve for \( S \):
Now, we equate the two expressions:
\[
S \times 0.92 = 36
\]
\[
S = \frac{36}{0.92} = \text{P}39.13
\]

### 4. Conclusion:
The manufacturer should sell each pound of canned meat for **P39.13** before applying the 8% discount to achieve a 20% profit on the selling price after the discount.

Would you like further details or have any questions?

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Here are 5 related questions:
1. How do you calculate profit margin if the selling price and cost are known?
2. What happens to the profit margin if the discount increases to 10%?
3. How would the selling price change if the cost per can increased by 10%?
4. How can a manufacturer determine the breakeven point for a product?
5. What is the difference between profit margin on cost and profit margin on selling price?

**Tip:** Always ensure the profit margin is calculated on the desired base (cost or selling price) to avoid confusion in pricing strategies.

Learn how to calculate the selling price of a product considering profit margin and discounts. This problem involves determining the selling price of canned meat to achieve a 20% profit margin after an 8% discount from a cost of P30 per can. Suitable for high school students studying business math.

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