Two pairs of different sizes contain 34.5 liters of water altogether. when 0.68 liter of water is poured from the bigger pail into the smaller pail, the amount of water in the bigger pail is 9 times that in the smaller pail. how much water was there in each pail at first?

There will always be 34.5L of water in the cups because no water is removed.
Therefore the cups still total 34.5L after the water is poured from one to the other.
The smaller cup has some amount of water we'll call x.
The larger cup has nine times this, so 9x.
We know that x + 9x = 34.5.
We can simplify this to 10x = 34.5.
Divide each side by 10...x = 3.45.
So, we know that the smaller cup had 3.45L of water at the end.
Since 0.68L was poured in, it must've started with 2.77L. (3.45 minus 0.68)
We can also conclude that the larger pail had 31.73L .
(35 minus 2.77, or 9 times 3.45 plus 0.68)