Question

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.(

Answer 1

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 \(\boxed{2.42}\).