To determine the minimum amount Raphael should charge per cup of punch to make a $10 profit, we first need to calculate his total costs.
Step 1: Calculate the cost of raspberry sorbet
- A gallon of sorbet is equivalent to 4 quarts.
- Raphael pays $4 for a quart of sorbet.
- Therefore, the cost for 1 gallon (4 quarts) of raspberry sorbet is: \[ 4 \text{ quarts} \times 4 \text{ dollars/quart} = 16 \text{ dollars} \]
Step 2: Calculate the cost of lemon-lime soda
- Raphael buys a 2 L container of lemon-lime soda for $3.
- Since he needs 2 liters, that will be: \[ 3 \text{ dollars} \]
Step 3: Calculate total costs
Now, we add these costs together to get the total cost: \[ \text{Total cost} = \text{Cost of sorbet} + \text{Cost of soda} = 16 \text{ dollars} + 3 \text{ dollars} = 19 \text{ dollars} \]
Step 4: Calculate total revenue needed for profit
Raphael wants to make a $10 profit. Thus, the total revenue he needs is: \[ \text{Total revenue needed} = \text{Total cost} + \text{Desired profit} = 19 \text{ dollars} + 10 \text{ dollars} = 29 \text{ dollars} \]
Step 5: Calculate price per cup
Raphael is making 12 cups of punch. To find the minimum price he should charge per cup, we divide the total revenue needed by the number of cups: \[ \text{Price per cup} = \frac{\text{Total revenue needed}}{\text{Number of cups}} = \frac{29 \text{ dollars}}{12} \]
Calculating that: \[ \frac{29}{12} \approx 2.4167 \]
Step 6: Rounding to nearest hundredth
When rounded to the nearest hundredth, that would be $2.42.
Final Answer
Therefore, the minimum amount Raphael should charge per cup of punch to make a $10 profit is: \[ \boxed{2.42} \]
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