we start with 3 quarts of lemon-lime soda and an unspecified amount of 45% fruit juice blend

we assume there is no fruit juice present in the 3 quarts of lemon-lime soda

let 'x' represent the amount, in quarts, of fruit juice blend added, then "0.45x" represents the amount of pure fruit juice in the final mixture

the final mixture has a volume of '3+x' quarts

the percentage of juice in the final mixture is the amount of pure juice (0.45x) divided by the total volume in the final mixture (3+x)

percentage of fruit juice in the final mixture is then:

0.3 = (0.45x)/(3+x)

solving for 'x' we have:

x = 6

6 quarts of the fruit juice blend must be added to produce a punch that is 30% juice