Question

Rafael is making punch and needs a gallon of sorbet and 2 liters of soda to make 12 cups. He pays $3.00 for a 2 liter of 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 quarts in a gallon

Answers

Answered by GPT-4o mini
To determine the minimum amount Rafael should charge per cup of punch to achieve a $10 profit, let's break down the costs involved and then calculate the price per cup.

### 1. **Costs of Ingredients:**
- **Sorbet:**
- 1 gallon of sorbet = 4 quarts
- Cost for 1 quart of sorbet = $4.00
- Total cost for 1 gallon (4 quarts) = 4 quarts * $4.00/quart = $16.00

- **Soda:**
- Cost for 2 liters of soda = $3.00 (given)

### 2. **Total Cost:**
- Total cost for both ingredients:
\[
\text{Total Cost} = \text{Cost of Sorbet} + \text{Cost of Soda}
\]
\[
\text{Total Cost} = 16.00 + 3.00 = 19.00
\]

### 3. **Total Required Profit:**
- Rafael wants to make a profit of $10. Therefore, the total amount he needs to earn is:
\[
\text{Total Earnings Required} = \text{Total Cost} + \text{Desired Profit}
\]
\[
\text{Total Earnings Required} = 19.00 + 10.00 = 29.00
\]

### 4. **Price Per Cup:**
- Rafael makes 12 cups of punch. So, to find the minimum price he should charge per cup:
\[
\text{Price per Cup} = \frac{\text{Total Earnings Required}}{\text{Number of Cups}}
\]
\[
\text{Price per Cup} = \frac{29.00}{12}
\]
\[
\text{Price per Cup} \approx 2.4167
\]

### 5. **Final Price:**
To ensure he covers costs and makes the desired profit, Rafael should charge at least $2.42 per cup (rounding up to the nearest cent).

### **Conclusion:**
Rafael should charge a minimum of **$2.42** per cup of punch to achieve a $10 profit.

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