tougher problems on simple equation

There are two mixtures of  acid and water, one of which contains twice as much water as acid, and  the other three times as much acid as water. How much must be taken from each in order to fill a liter measure, in which the water and the acid shall be equally mixed?








Answer:

Basis: 1 liter of mixture in each of the three bottles.

Bottle 1:
1/ 3 acid and 2/3 water.

Bottle 2:
3/4 acid and 1/4 water

bottle 3:

1/2 acid and 1/2 water


Let x  amount of solution from bottle 1 be transferred to bottle 3.

Therefore, Amount of solution added from bottle 2 = 1 - x 

Comparing acid concentration, we have

(1/3)x + (3/4) (1- x) = 1/2

or, (5/12)x = 1/4

or, x = 3/5 liter

So, from bottle 1, 3/5 liters and from bottle 2 (1 - 3/5) = 2/5 liter