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 pound of canned meat, let's break down the problem step by step.

### Given:
- **Cost per can (C):** P30
- **Desired profit:** 20% on the selling price
- **Discount:** 8% on the selling price

### Let \( S \) be the selling price per pound of canned meat before discount.

1. **After applying the discount:**
   \[
   \text{Discounted Price} = S - 0.08S = 0.92S
   \]

2. **The profit is based on the selling price (not the cost). Therefore, the cost plus profit equals the discounted selling price:**
   \[
   \text{Cost} = \text{Discounted Price} \times (1 - \text{Profit Margin})
   \]
   \[
   P30 = 0.92S \times (1 - 0.20)
   \]

3. **Simplifying:**
   \[
   P30 = 0.92S \times 0.80
   \]
   \[
   P30 = 0.736S
   \]

4. **Solving for \( S \):**
   \[
   S = \frac{P30}{0.736} \approx P40.76
   \]

### Conclusion:
The manufacturer should sell the canned meat for approximately **P40.76** per pound before the discount to achieve a 20% profit margin after providing an 8% discount.

Would you like any further details or have any questions?

### Related Questions:
1. How does changing the profit margin affect the final selling price?
2. What would the selling price be if the discount were 10% instead of 8%?
3. How much profit does the manufacturer make per can at this selling price?
4. How would the selling price change if the cost per can increased to P35?
5. What if the manufacturer wants to include a tax of 12% on the selling price?

### Tip:
Always ensure that the profit margin is calculated on the selling price, not on the cost price, when determining the final price after discounts.

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

Find out how to calculate the selling price for canned meat to achieve a 20% profit margin after an 8% discount. This problem covers essential concepts in algebra, profit and loss, and percentage calculations, suitable for Grades 9-12 students.

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