How much of a brand A fruit punch (35% fruit juice) must be mixed with 9L of grape juice to create a mixture containing 74% fruit juice?

Grape juice is 100% fruit juice so for 9 liters of grape juice you have 9 liters of fruit juice

9 liters fruit juice

9 liters juice

for every liter you add of fruit punch, you get. 35 liters of fruit juice. so the question is how many liters of punch (we'll say x liters) do you have to add to get the ratio of fruit juice to total juice to be 74 to 100?

9 liters of fruit juice + 0.35x = 74

9 liters of juice + x 100

cross multiply

(9 + 0.35x) 100 = (9 + x) 74

900 + 35x = 666 + 74x

234 = 39x

x=6 liters of brand A fruit punch