SOLUTION: How many liters of 30% alcohol solution must be mixed with 70 liters of 70% solution to get a 50% solution?

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: How many liters of 30% alcohol solution must be mixed with 70 liters of 70% solution to get a 50% solution?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 178448: How many liters of 30% alcohol solution must be mixed with 70 liters of 70% solution to get a 50% solution?
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
let x and y be the 30% and 70% solutions respectively
:
x+y=70......eq 1
.3x+.7y=.5(70)...eq 2
:
take eq 1 and rewrite it to y=70-x and plug it into eq 2
:
.3x+.7(70-x)=.5(70)
:
.3x+49-.7x=35
:
-.4x=-14
:
highlight%28x=35%29liters of 30% solution
:
highlight%28y=70-35=35%29liters of 70% solution
:
we really could have come up with this by common sense. 50% is half way between
30% and 70% so to have equal portions makes total sense