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? Your answer should be a dollar amount rounded to the nearest hundredth
To make 12 cups of punch, Rafael needs 2 liters * (1 gallon/3.78541 liters) = <<2*1/3.78541=0.528=0.53>>0.53 gallons of raspberry sorbet.
To make 12 cups of punch, Rafael needs to make 3.78541 liters * (1000 mL/1 liter) = <<3.78541*1000=3785.41>>3785.41 mL of lemon-lime soda.
Each cup of punch requires 3785.41 mL / 12 cups = <<3785.41/12=315.45166666666665>>315.45 mL of lemon-lime soda.
He pays $3.00 / 2 liters = $1.50 for 315.45 mL of lemon-lime soda.
So the cost of the lemon-lime soda per cup of punch is $1.50 / 12 cups = $0.125 per cup.
He pays $4.00 / (1 quart/ 4 cups) = $1.00 for 0.53 gallons of raspberry sorbet per cup of punch.
So the cost of the raspberry sorbet per cup of punch is $1.00 / 12 cups = $0.08333333333333333 per cup.
Together, the cost of the lemon-lime soda and raspberry sorbet is $0.125 + $0.08333333333333333 = $0.20833333333333331 per cup.
To make a $10 profit, he needs to charge $0.20833333333333331 + $10 = $10.208333333333335.
Therefore, he should charge approximately $10.21 per cup of punch to make a $10 profit. Answer: \boxed{10.21}.