The amount of alcohol divided by the total amount of solution is the % alcohol in the solution.
It's alcohol/total solution = % (written as a decimal).
There is x ounces of the 35% solution and 18 ounces of the 40% solution. When added together this is 18+x. That's the total amount of the solution.
The amount of alcohol in x ounces of 35% alcohol solution is .35x ounces.
The amount of alcohol in 18 ounces of 40% alcohol solution is .4*18=7.2 ounces.
The total amount of alcohol in the combined solution is .35x + 7.2
The % it equals is 37% or .37
(.35x+7.2)/(18+x) = .37
.35x + 7.2 = .37(18+x)
.35x + 7.2 = 6.66 + .37x
.54 = .02x
x=.54/.02 = 27 ounces.
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