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?

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

1. **Calculate the cost of the raspberry sorbet:**
- Rafael needs 1 gallon of sorbet.
- There are 4 quarts in a gallon.
- The cost of 1 quart of sorbet is $4.00, so the total cost for 1 gallon (which is 4 quarts) is:
\[
4 \text{ quarts} \times 4.00 \text{ dollars/quart} = 16.00 \text{ dollars}
\]

2. **Calculate the cost of the lemon-lime soda:**
- Rafael needs 2 liters of soda.
- The cost for a 2-liter container of soda is $3.00.

3. **Calculate the total cost of the ingredients:**
\[
\text{Total cost} = \text{Cost of sorbet} + \text{Cost of soda}
\]
\[
\text{Total cost} = 16.00 + 3.00 = 19.00 \text{ dollars}
\]

4. **Calculate the total cost including profit:**
- Rafael wants to make a profit of $10. Therefore, the total amount he needs to cover is:
\[
\text{Total amount to cover} = \text{Total cost} + \text{Profit}
\]
\[
\text{Total amount to cover} = 19.00 + 10.00 = 29.00 \text{ dollars}
\]

5. **Calculate the price per cup:**
- Rafael is making 12 cups of punch. Thus, the price per cup is calculated as follows:
\[
\text{Price per cup} = \frac{\text{Total amount to cover}}{\text{Number of cups}} = \frac{29.00}{12}
\]
\[
\text{Price per cup} \approx 2.41667
\]

6. **Round to the nearest hundredth:**
- Rounding 2.41667 to the nearest hundredth gives approximately **$2.42**.

Therefore, the minimum amount Rafael should charge per cup of punch to make a $10 profit is **$2.42**.

it is not $2.42 or $3.00

Let’s reevaluate the calculations step by step to ensure accuracy.

1. **Calculate the cost of raspberry sorbet:**
- Rafael needs 1 gallon of raspberry sorbet.
- There are 4 quarts in a gallon.
- The cost of one quart of sorbet is $4.00.
- Therefore, the total cost for 1 gallon of sorbet is:
\[
4 \text{ quarts} \times 4.00 \text{ dollars/quart} = 16.00 \text{ dollars}
\]

2. **Calculate the cost of lemon-lime soda:**
- Rafael needs 2 liters of lemon-lime soda.
- The cost for a 2-liter container of soda is $3.00.

3. **Calculate the total cost of the ingredients:**
\[
\text{Total cost} = \text{Cost of sorbet} + \text{Cost of soda}
\]
\[
\text{Total cost} = 16.00 + 3.00 = 19.00 \text{ dollars}
\]

4. **Calculate the total amount needed for profit:**
- Rafael wants to make a profit of $10. Therefore, the total amount he needs to cover is:
\[
\text{Total amount to cover} = \text{Total cost} + \text{Profit}
\]
\[
\text{Total amount to cover} = 19.00 + 10.00 = 29.00 \text{ dollars}
\]

5. **Calculate the price per cup:**
- Rafael is making 12 cups of punch. Thus, the price per cup can be calculated as follows:
\[
\text{Price per cup} = \frac{\text{Total amount to cover}}{\text{Number of cups}} = \frac{29.00}{12}
\]
\[
\text{Price per cup} \approx 2.41667 \text{ dollars}
\]

6. **Round to the nearest hundredth:**
- Rounding 2.41667 to the nearest hundredth gives approximately **$2.42**.

The price of **$2.42** is indeed correct according to the provided calculations. If you believe there’s an error or you're looking for a different result, please clarify if there are additional costs or factors involved that I may not have considered. Thank you!