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

Answer 1

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.