How much of a 55% orange juice drink must be mixed with 100 gallons of a 45 % orange juice drink to obtain a mixture that is 50% orange​ juice?

x = amount of 55%

100-x = amount of 45%

x(.55) + (100-x)(.45) = 100 (.5)

.55x + 45 - .45x = 50

.1 x = 5

 x= 50 gallons      (although you can mix INFINITE gallons of 'orange juice DRINK' and never make orange JUICE    haha)

Let x  = the number of gallons of 55% juice to be mixed....and we have

.55(x )  + .45(100) = .50(x + 100)     simplify

.55x + 45  = .50x + 50     subtract .50x, 45 from both sides

.05x  =  5        divide both sides by .05

x  = 100 gallons of the 55% juice

{This makes sense when you think about it....equal amounts of 45% juice and 55% juice should produce a mixture with an "average" percentage of the two }

Sorry!   I misread the question..... I was MAKING 100 gallons of 50% juice, not MIXING with 100 gallons of 45% juice!!