1.) A water is purification plant works by passing the dirty water through three filters in turn. The first takes out all but 1/4 of the dirt in the water, the second leaves 1/5 of the dirt reaching it and the last takes out 2/3 of what's left.

(a) What fraction of the dirt is left in the water after it has gone through the plant?

(b) What fraction of the dirt has the plant removed?

Let x = total dirt in the water before it passed any filter.

After passing the first filter, (1/4)x or x/4 is left.

After passing the second filter, (1/5) of (x/4) is left

That is (1/5)*(x/4) = (1*x)/(5*4) = x/20 is left.

Finally, after the 3rd filter, 2/3 of x/20 is removed.

So 1/3 of x/20 is left, or (1/3)*(x/20) = (1*x)/(3*20) = x/60 is left.

(a) What fraction of the dirt is left in the water after it has gone through the plant?

x/60 or 1/60 of the dirt. --------------answer.

(b) What fraction of the dirt has the plant removed?

x -x/60

= x/1 -x/60

= (60*x -x)60

= (59x)/60

Therefore, 59/60 of the dirt is removed.