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 that will allow the manufacturer to make a 20% profit after giving away an 8% discount, we can follow these steps:

### 1. Set up the variables:
- Let \( S \) be the initial selling price before the discount.
- The manufacturer wants a 20% profit on the selling price.

### 2. Account for the 8% discount:
- After applying an 8% discount, the actual price the customer pays is \( 0.92S \).

### 3. Account for the 20% profit:
- The cost of the canned meat is \( \text{P}30 \). 
- The manufacturer wants a 20% profit on the selling price, so the profit should be \( 0.20S \).
- Therefore, the actual revenue (price after discount) minus the cost should equal the desired profit:
  \[
  0.92S = \text{Cost} + \text{Profit}
  \]
  \[
  0.92S = 30 + 0.20S
  \]

### 4. Solve for \( S \):
- Rearrange the equation to isolate \( S \) on one side:
  \[
  0.92S - 0.20S = 30
  \]
  \[
  0.72S = 30
  \]
  \[
  S = \frac{30}{0.72}
  \]
  \[
  S = 41.67
  \]

### 5. Calculate the selling price after the discount:
- The manufacturer should set the initial selling price at \( \text{P}41.67 \) to achieve the desired profit after discount.

Thus, the manufacturer should sell the canned meat at **P41.67 per pound** before applying the 8% discount to ensure a 20% profit after the discount.

Would you like more details or have any questions?

### Related Questions:
1. What would the selling price be if the manufacturer wanted a 30% profit instead?
2. How does the required selling price change if the discount increases to 10%?
3. What if the cost per can increases to P35? How does that affect the selling price?
4. How much profit will the manufacturer make per can with the calculated selling price?
5. How would the selling price change if no discount is applied?

**Tip:** Always check how discounts affect the final profit when setting a selling price.

Learn how to calculate the selling price per pound of canned meat to achieve a 20% profit after giving an 8% discount. Step-by-step solution provided with detailed calculations and formulas. Suitable for college-level students and professionals.

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