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 find out the selling price of a pound of canned meat that allows the manufacturer to make a 20% profit after giving an 8% discount, let's break down the problem step by step.

### Step 1: Let \( S \) be the selling price (before discount) of the canned meat.

### Step 2: Calculate the discounted price.
The manufacturer offers an 8% discount, so the price after the discount is:
\[
\text{Discounted Price} = S - (0.08 \times S) = 0.92S
\]

### Step 3: Determine the cost and desired profit.
The cost of the product is \( P30 \). The manufacturer wants to make a 20% profit on the selling price, so the profit should be 20% of the discounted price. Thus, the cost plus the profit should equal the discounted price:
\[
\text{Discounted Price} = \text{Cost} + \text{Profit}
\]
\[
0.92S = P30 + 0.2 \times S
\]

### Step 4: Solve for \( S \).
We rearrange the equation to solve for \( S \):
\[
0.92S = 30 + 0.2S
\]
Subtract \( 0.2S \) from both sides:
\[
0.92S - 0.2S = 30
\]
\[
0.72S = 30
\]
Now, divide both sides by 0.72:
\[
S = \frac{30}{0.72} = 41.67
\]

### Conclusion:
The manufacturer should sell the canned meat at \( P41.67 \) per pound before discount in order to achieve a 20% profit after giving an 8% discount.

Would you like more details on any step, or have any questions?

Here are 5 related questions for further exploration:

1. What would the selling price be if the manufacturer wanted a 25% profit instead of 20%?
2. How does the profit change if the discount is increased to 10%?
3. What is the breakeven price if no discount is offered?
4. How would the profit percentage change if the cost per can increased by 10%?
5. What is the effect of removing the discount altogether on the selling price?

**Tip:** When calculating profits involving discounts, always adjust for the discount before calculating the desired profit margin.

Learn how to calculate the selling price of canned meat to achieve a 20% profit after an 8% discount. This problem covers profit calculation, percentage adjustments, and discount effects. Suitable for high school students (Grades 9-12).

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