To determine the minimum amount Rafael should charge per cup of punch to achieve a $10 profit, let's break down the costs involved and then calculate the price per cup.
1. Costs of Ingredients:
-
Sorbet:
- 1 gallon of sorbet = 4 quarts
- Cost for 1 quart of sorbet = $4.00
- Total cost for 1 gallon (4 quarts) = 4 quarts * $4.00/quart = $16.00
-
Soda:
- Cost for 2 liters of soda = $3.00 (given)
2. Total Cost:
- Total cost for both ingredients: \[ \text{Total Cost} = \text{Cost of Sorbet} + \text{Cost of Soda} \] \[ \text{Total Cost} = 16.00 + 3.00 = 19.00 \]
3. Total Required Profit:
- Rafael wants to make a profit of $10. Therefore, the total amount he needs to earn is: \[ \text{Total Earnings Required} = \text{Total Cost} + \text{Desired Profit} \] \[ \text{Total Earnings Required} = 19.00 + 10.00 = 29.00 \]
4. Price Per Cup:
- Rafael makes 12 cups of punch. So, to find the minimum price he should charge per cup: \[ \text{Price per Cup} = \frac{\text{Total Earnings Required}}{\text{Number of Cups}} \] \[ \text{Price per Cup} = \frac{29.00}{12} \] \[ \text{Price per Cup} \approx 2.4167 \]
5. Final Price:
To ensure he covers costs and makes the desired profit, Rafael should charge at least $2.42 per cup (rounding up to the nearest cent).
Conclusion:
Rafael should charge a minimum of $2.42 per cup of punch to achieve a $10 profit.