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, we need to account for both the desired profit and the discount given to customers.

### Step 1: Determine the selling price before discount
Let \( S \) be the selling price before the discount. The manufacturer wants to make a 20% profit on the selling price.

The profit equation is:

\[
\text{Cost Price} = (1 - 0.20) \times S
\]

Given that the cost price is \( P30 \):

\[
30 = 0.80 \times S
\]

Solve for \( S \):

\[
S = \frac{30}{0.80} = 37.50
\]

### Step 2: Account for the discount
The manufacturer gives an 8% discount on the selling price \( S \). The final selling price after discount is:

\[
\text{Final Selling Price} = S \times (1 - 0.08) = 37.50 \times 0.92 = P34.50
\]

### Conclusion
The food manufacturer should sell the canned meat for **P37.50** per pound before the discount. After applying the 8% discount, the customer will pay **P34.50** per pound, ensuring that the manufacturer still achieves a 20% profit margin on the original selling price.

Would you like further details or have any questions?

Here are some related questions you might consider:
1. What would be the selling price if the desired profit margin were 25% instead of 20%?
2. How would the selling price change if the discount increased to 10%?
3. What is the profit in pesos when selling 100 cans at the calculated price?
4. How would you calculate the break-even point for the manufacturer?
5. What is the effect of increasing production costs on the selling price?

**Tip:** When calculating prices with discounts and profit margins, always determine the base selling price before applying discounts to ensure your profit goals are met.

Learn how to calculate the selling price of canned meat with a 20% profit margin and an 8% discount. Follow step-by-step calculations to ensure profitability while considering customer discounts.

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