To determine the minimum amount Rafael should charge per cup of punch to make a $10 profit, we first need to calculate his total costs for the ingredients used in making the punch.
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Cost of Sorbet:
- Since Rafael needs a gallon of raspberry sorbet and there are 4 quarts in a gallon, he needs 4 quarts of sorbet.
- Given that each quart of sorbet costs $4.00, the total cost for the sorbet is: \[ \text{Total cost of sorbet} = 4 , \text{quarts} \times 4.00 , \text{dollars/quart} = 16.00 , \text{dollars}. \]
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Cost of Lemon-Lime Soda:
- Rafael needs 2 liters of lemon-lime soda and pays $3.00 for a 2-liter container, so: \[ \text{Total cost of soda} = 3.00 , \text{dollars}. \]
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Total Cost:
- The total cost for both the sorbet and the soda is: \[ \text{Total cost} = \text{Cost of sorbet} + \text{Cost of soda} = 16.00 , \text{dollars} + 3.00 , \text{dollars} = 19.00 , \text{dollars}. \]
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Total Revenue to Achieve Desired Profit:
- Rafael wants to make a profit of $10. Therefore, the total revenue that he needs to generate is: \[ \text{Total revenue needed} = \text{Total cost} + \text{Desired profit} = 19.00 , \text{dollars} + 10.00 , \text{dollars} = 29.00 , \text{dollars}. \]
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Price Per Cup:
- Since the punch makes 12 cups, the minimum amount he should charge per cup is calculated by dividing the total revenue needed by the number of cups: \[ \text{Price per cup} = \frac{\text{Total revenue needed}}{\text{Number of cups}} = \frac{29.00 , \text{dollars}}{12 , \text{cups}} \approx 2.4167 , \text{dollars/cup}. \]
- Rounding up to the nearest cent, the price per cup should be: \[ \text{Price per cup} = 2.42 , \text{dollars}. \]
Thus, the minimum amount Rafael should charge per cup of punch to make a $10 profit is approximately $2.42.
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