Rafael is making punch and needs a gallon of raspberry sorbet and 2 liters of Sprite to make 12 cups. He pays $3.00 for a 2-liter container of Sprite 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?

Answer 1

To make 12 cups of punch, Rafael needs 12 cups * 1 gallon / 16 cups/gallon = <<12*1/16=0.75>>0.75 gallons of raspberry sorbet.
He needs 2 liters * 1 gallon/3.78541 liters = <<2*1/3.78541=0.52834>>0.52834 gallons of Sprite.
Therefore, the total volume of liquid in the punch is 0.75 gallons + 0.52834 gallons = <<0.75+0.52834=1.27834>>1.27834 gallons.
Thus, Rafael is making 1.27834 gallons * 16 cups/gallon = <<1.27834*16=20.45344>>20.45344 cups of punch.
The raspberry sorbet costs $4.00/quart * 1 quart/4 cups * 20.45344 cups = $20.45.
The Sprite costs $3.00/2 liters * 2 liters/67.6280451 ounces * 33.8140226 ounces/liter * 20.45344 cups = $20.45.
Thus, the total cost is $20.45 + $20.45 = $<<20.45+20.45=40.90>>40.90.
Rafael wants to make a $10 profit, so he should charge $40.90 + $10 = $<<40.90+10=50.90>>50.90.
Since there are 12 cups of punch, Rafael should charge $50.90 / 12 cups = $<<50.90/12=4.24>>4.24 per cup. Answer: \boxed{4.24}.