Rafael is making punch and needs a gallon of raspberry sherbet and 2 L of lemon lime soda to make 12 cups. He pays three dollars for a 2 L container of lemon lime soda and four dollars for a quarter of sherbet. What is the minimum amount he should charge per cup of punch to make $10 profit. Remember there are courts in a gallon. Your answer should be a dollar amount rounded to the nearest 10.

To make 12 cups of punch, Rafael needs 1 gallon of raspberry sherbet (which is 4 quarts) and 2 L of lemon-lime soda (which is 2.11 quarts).

Therefore, Rafael needs to charge for a total of 4 + 2.11 = <<4+2.11=6.11>>6.11 quarts of punch.

Rafael paid $4 for the sherbet and $3 for the soda, meaning he spent a total of $4 + $3 = $7.

To make a $10 profit, Rafael needs to charge $7 + $10 = $17 in total.

Since he is making 12 cups of punch, he needs to charge a minimum of $17 / 12 = $1.42 per cup.

Rounded to the nearest 10, the minimum amount Rafael should charge per cup of punch to make a $10 profit is $1.40. Answer: \boxed{1}.