Rafael is making punch tea needs a gallon of raspberry sorbet and 2 L of lemon lime soda to make 12 cups. He pays three dollars for a 2 L container of lemon lime soda and four dollars for a quart of sorbet. What is the minimum amount he should charge per cup of punch to make a $10 profit?

Answer 1

To determine the minimum amount Rafael should charge per cup of punch to make a $10 profit, we first need to calculate his costs for the ingredients.

1. Costs of Ingredients:

   • Raspberry Sorbet:

     • Rafael needs 1 gallon of raspberry sorbet. Since there are 4 quarts in a gallon, he needs 4 quarts.
     • At a cost of $4 per quart, the cost for the sorbet is: \[ 4 , \text{quarts} \times 4 , \text{dollars/quart} = 16 , \text{dollars} \]

   • Lemon Lime Soda:

     • Rafael needs 2 liters of lemon lime soda.
     • The cost for a 2 L container is $3. Thus, the soda cost is: \[ 3 , \text{dollars} \]

2. Total Costs:

   • Total cost for both ingredients: \[ 16 , \text{dollars (sorbet)} + 3 , \text{dollars (soda)} = 19 , \text{dollars} \]

3. Desired Profit:

   • Rafael wants to make a profit of $10. Therefore, the total amount he needs to charge to cover costs and profits is: \[ 19 , \text{dollars (costs)} + 10 , \text{dollars (profit)} = 29 , \text{dollars} \]

4. Determine the Price per Cup:

   • Rafael makes a total of 12 cups of punch. To find the cost per cup, we divide the total amount he needs to charge by the number of cups: \[ \text{Price per cup} = \frac{29 , \text{dollars}}{12 , \text{cups}} \approx 2.41667 , \text{dollars} \]

5. Round Up to the Nearest Cent:

   • Since he needs to charge a whole cent, it's logical to round up to the nearest cent. This means he should charge: \[ \text{Rounded price per cup} = 2.42 , \text{dollars} \]

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