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 rounding to the nearest hundredth
First, we need to convert the measures of raspberry sorbet and lemon-lime soda to the same unit. Since there are 4 cups in a quart, and we need 12 cups total, we need 12/4 = 3 quarts of sorbet
Since there are 128 ounces in a gallon, and 32 ounces in a quart, we need 3*32 = 96 ounces of sorbet
Since there are 128 ounces in a gallon, and 128/12 = 10.67 ounces in a cup, we need 10.67*12 = <<10.67*12=128>>128 ounces of punch
Since there are 2 liters in a 2-liter container of lemon-lime soda, we need 2*12/3 = <<2*12/3=8>>8 containers of lemon-lime soda
Since there are 128 ounces in a gallon and 128/33.8 = 3.78541 liters in a gallon, we need 2*8/3.78541 = <<2*8/3.78541=4.226755>>4.23 L of lemon-lime soda
Since we have 128 ounces of punch and 128/33.8 = 3.78278 L in a gallon, we need 12*10/3.78541 = <<12*10/3.78541=31.71758>>31.72 L of punch
Rafael got 2 liters of lemon-lime soda at $3.00, so he paid 3/2 = $1.50 per liter
Rafael got 3 quarts of sorbet at $4.00 per quart, so he paid 4*3 = $12.00 for sorbet
Rafael got 4.23 liters of lemon-lime soda at $1.50 per liter, so he paid 4.23*1.50 = $6.35 for lemon-lime soda
Rafael got 31.72 liters of punch at $4.00, so he paid 31.72*4 = $126.88 for punch
To make a $10 profit, Rafael needs to charge 126.88+6.35+12.00+10 = $155.23
Since there are 128 ounces in a gallon and 128/12 = 10.67 ounces in a cup, Rafael needs to charge 155.23/12 = $<<155.23/12=12.94>>12.94 per cup of punch. Answer: \boxed{12.94}.