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 per can of meat, given the manufacturer's cost and desired profit margin, we can follow these steps:

1. **Identify the cost price and desired profit margin:**
   - The cost price per can: \( P30 \)
   - Desired profit margin: \( 20\% \)
   - Discount offered: \( 8\% \)

2. **Calculate the required profit on the selling price:**
   - Let the final selling price (after discount) be \( S \).
   - The desired profit is \( 20\% \) of the final selling price, which is \( 0.20 \times S \).

3. **Calculate the selling price before discount:**
   - Let the original selling price (before the discount) be \( P \).
   - After an \( 8\% \) discount, the selling price becomes \( S = P \times (1 - 0.08) = 0.92P \).

4. **Set up the profit equation:**
   - The manufacturer wants a \( 20\% \) profit on the selling price after the discount:
     \[
     \text{Cost} + \text{Profit} = S
     \]
     \[
     30 + 0.20S = S
     \]

5. **Substitute \( S = 0.92P \) into the profit equation:**
   \[
   30 + 0.20 \times 0.92P = 0.92P
   \]
   \[
   30 + 0.184P = 0.92P
   \]

6. **Solve for \( P \):**
   \[
   30 = 0.92P - 0.184P
   \]
   \[
   30 = 0.736P
   \]
   \[
   P = \frac{30}{0.736}
   \]
   \[
   P \approx 40.76
   \]

Therefore, the food manufacturer should sell each can of meat for approximately **P40.76** before the 8% discount is applied to achieve a 20% profit margin on the selling price.

### Do you want more details or have any questions?

### Related Questions:

1. How would the selling price change if the desired profit margin was 25% instead of 20%?
2. What would be the selling price if no discount was offered, maintaining the same profit margin?
3. How much profit does the manufacturer make per can with the calculated selling price?
4. How does the discount percentage affect the final profit margin?
5. If the cost price increased to P35 per can, what would be the new selling price to maintain a 20% profit margin after the discount?

### Tip:

When dealing with profit margins and discounts, always consider how each affects the selling price separately to ensure accurate calculations.

Learn how to calculate the selling price per can of meat with a 20% profit margin after an 8% discount. Understand the step-by-step process involving cost price, profit margin, and discount calculations. Suitable for high school students and anyone interested in business math.

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