Rafael is making punch and needs a gallon of raspberry sorbet and 2 liters of lemon-lime soda to make 12 cups. He pays $3.00 for a 2-liter container of lemon-lime soda and $4.00 for a quart of sorbet. What is the minimum amount he should charge per cup of punch to make a $10 profit? (Remember there are 4 quarts in a gallon.) Your answer should be a dollar amount rounded to the nearest hundredth.(

To determine the minimum amount Rafael should charge per cup of punch to achieve a $10 profit, we first need to calculate the total cost of the ingredients.

1. Cost of raspberry sorbet:

   • Rafael needs 1 gallon of raspberry sorbet.
   • Since there are 4 quarts in a gallon, Rafael needs to buy 4 quarts.
   • The cost per quart of sorbet is $4.00.
   • Therefore, the total cost for sorbet is: [ \text{Total cost for sorbet} = 4 , \text{quarts} \times 4.00 , \text{dollars/quart} = 16.00 , \text{dollars}. ]

2. Cost of lemon-lime soda:

   • Rafael needs 2 liters of lemon-lime soda.
   • The cost per 2-liter container is $3.00.
   • Therefore, the total cost for soda is: [ \text{Total cost for soda} = 3.00 , \text{dollars}. ]

3. Total cost of ingredients:

   • Now, we can sum the costs of both ingredients: [ \text{Total cost} = \text{Cost of sorbet} + \text{Cost of soda} = 16.00 + 3.00 = 19.00 , \text{dollars}. ]

4. Desired profit:

   • Rafael wants to make a $10 profit, so we add this to the total cost: [ \text{Total amount needed} = \text{Total cost} + \text{Profit} = 19.00 + 10.00 = 29.00 , \text{dollars}. ]

5. Charge per cup:

   • Rafael makes 12 cups of punch. Therefore, to find the charge per cup, we divide the total amount needed by the number of cups: [ \text{Charge per cup} = \frac{\text{Total amount needed}}{\text{Number of cups}} = \frac{29.00}{12} \approx 2.4167 , \text{dollars}. ]

6. Rounding:

   • Rounding to the nearest hundredth, we find: [ \text{Charge per cup} \approx 2.42 , \text{dollars}. ]

Thus, the minimum amount Rafael should charge per cup of punch to make a $10 profit is (\boxed{2.42}).