Question 821488: two vessels contain mixtures of sulphuric acid and distilled water, one of which contains twice as much as water as acid, and the other three times as much acid as water. how much must there be taken from each to fill a one litre cup, in which the acid and water shall be equally mixed?
Answer by ankor@dixie-net.com(22740)   (Show Source):
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two vessels contain mixtures of sulfuric acid and distilled water,
we can do this in percent acid
:
one of which contains twice as much as water as acid,
this solution is 33% acid (.33)
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and the other three times as much acid as water.
this one is 75% acid (.75)
:
how much must there be taken from each to fill a one litre cup, in which the acid and water shall be equally mixed?
:
let x = amt of the 1st solution (in liters)
the resulting amt is to 1 liter, therefore
(1-x) = amt of the 2nd solution
:
A typical mixture equation
.33x + .75(1-x) = .50(1)
.33x + .75 - .75x = .5
.33x - .75x = .5 - .75
-.42x = -.25
x = -.25/-.42
x ~ .6 liters of the 1st solution
then
1 - .6 = .4 liters of the 2nd solution
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