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?
First find the total cost per gallon of raspberry sorbet by multiplying the price per quart by the number of quarts per gallon: $4.00/quart * 4 quarts/gallon = $<<4*4=16.00>>16.00/gallon
Then find how many gallons of sorbet Rafael needs by dividing the number of cups by the number of cups per gallon: 12 cups * 1 gallon/16 cups = <<12*1/16=0.75>>0.75 gallons
Multiply that number by the cost per gallon to find the total cost of the sorbet: 0.75 gallons * $16.00/gallon = $<<0.75*16=12.00>>12.00
Then find the total cost of the Sprite by multiplying the cost per liter by the number of liters: $3.00/liter * 2 liters = $<<3*2=6.00>>6.00
Then add the cost of the sorbet and the Sprite to find the total cost: $6.00 + $12.00 = $<<6+12=18.00>>18.00
Then add the desired profit to the cost to find the selling price: $18.00 + $10.00 = $<<18+10=28.00>>28.00
Finally, divide the selling price by the number of cups to find the price per cup: $28.00 / 12 cups = $<<28/12=2.3333333333333335>>2.33/cup. Answer: \boxed{2.33}.