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 qua

Question

rts 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 make a $10 profit, we first need to calculate his total costs in making the punch.

Step 1: Calculate the cost of raspberry sorbet

Rafael needs 1 gallon of raspberry sorbet.

1 gallon = 4 quarts. Since the cost is $4.00 for 1 quart:

Cost of sorbet = 4 quarts × $4.00/quart = $16.00.

Step 2: Calculate the cost of lemon-lime soda

Rafael needs 2 liters of lemon-lime soda.

He pays $3.00 for a 2-liter container. Thus, the cost of the soda is simply:

Cost of soda = $3.00.

Step 3: Calculate total costs

Now, we can find the total costs for making the punch:

Total cost = Cost of sorbet + Cost of soda
Total cost = $16.00 + $3.00 = $19.00.

Step 4: Calculate the total revenue for the desired profit

Rafael wants to make a $10 profit. Thus, he needs to cover his total costs plus the desired profit.

Total revenue needed = Total cost + Desired profit
Total revenue needed = $19.00 + $10.00 = $29.00.

Step 5: Calculate the price per cup

Finally, Rafael will make 12 cups of punch. We can find the minimum amount he should charge per cup by dividing the total revenue needed by the number of cups:

Price per cup = Total revenue needed / Number of cups
Price per cup = $29.00 / 12 = $2.41666...

Step 6: Round the price

Rounding to the nearest hundredth:

Price per cup ≈ $2.42.

Conclusion

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