Raphael 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?

Answer 1

First find the number of liters in 12 cups: 12 cups * 1 liter / 4 cups = <<12*1/4=3>>3 liters
Then divide the total cost of the soda by the number of liters to find the cost per liter: $3.00 / 2 liters = $<<3/2=1.50>>1.50/liter
Multiply the number of liters by the cost per liter to find the total cost of the soda: 3 liters * $1.50/liter = $<<3*1.5=4.50>>4.50
Then multiply the cost per quart of sorbet by the number of quarts to find the total cost of the sorbet: $4.00/quart * 1 gallon/4 quarts = $<<4*1/4=1>>1.00
Then add the cost of the soda and sorbet to find the total cost: $4.50 + $1.00 = $<<4.5+1=5.50>>5.50
Then add the desired profit to find the total price he should charge: $10.00 + $5.50 = $<<10+5.5=15.50>>15.50
Finally, divide the total price by the number of cups to find the price per cup: $15.50 / 12 cups = $<<15.5/12=1.29>>1.29. Answer: \boxed{1.29}.