A pail contained 3.68L of water more than a bottle. After Bill poured away 1.2L of water from the pail, the pail contained 3 times as much water as the bottle. (a) How much more water did the pail contain than the bottle in the end? (b) How much water did thr bottle contain?

(a) Since initially the pail contained 3.68L of water more than the bottle and then Bill poured away 1.2L from the pail but didn't change the content of the bottle, then to calculate how much more water the pail contains than the bottle in the end, you simply subtract the water Bill removed from the pail from the initial excess of water the pail had:

[tex]3.68-1.2=2.48[/tex]

So, in the end the pail contains 2.48L of water more than the bottle.

(b) To solve this we're going to do a simple system of two equations. The first equation is given by the excess of water the pail has (the bottle has 2.48L less than the pail, so to equal the contents it's necessary to add 2.48L to the bottle); the second equation is given by the 1:3 relation between the water in the pail and the water in the bottle (the pail contains 3 times as much as the bottle, so to equal the contents it's necessary to multiply the content of the bottle by 3). In this case, "y" will represent the water in the pail, and "x" represents the water in the bottle:

[tex]\left \{ {{y=2.48+x} \atop {y=3x}} \right.[/tex]

This system can be solved by equalizing the first and second expression:

[tex]2.48+x=3x\\2x=2.48\\x=1.24[/tex]

So, the bottle contained 1.24L of water.