Question 1059451
So, we don't know how much alcohol was added to the mixture. Let's call the amount of alcohol x. And 1x, or simply x is pure alcohol. Now, 0.40(50) is the quantity at 40% and x+0.40(50) is when we add the pure alcohol (x) to the mixture.
:
Next, we know that a quantity of alcohol x was added to 50 gallons. So we know the final quantity will be x+50. But what will be the concentration in that final mixture? We don't know. Let's call the concentration in the final 
mixture y. Put it all together:
:
x+0.40(50) = y(x+50)
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John