Gallons: x+y=60 and thus x=60-y
Amount of alcohol. .2x + .5y = .4*60 = 24. This makes sense because 60 gallons of a 40% solution has 24 gallons of alcohol in it. 24/60 = .4
Substitute x in terms of y from the gallons equation into the amount equation:
.2(60-y) +.5y =24 ---> 12 -.2y +.5y = 24 ---> .3y = 12 ---> y = 40.
Substitute y=40 into the gallons equation x+40 = 60 ---> x =20
20 gallons of 20% solution mix with 40 gallons of 50% solution to give 60 gallons of 40% solution.
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