The amount of antifreeze in the radiator at the start is #10%# of #5# litres, that is
#0.1*5 = 0.5# litres.
If we remove #x# litres of liquid, then assuming the antifreeze is uniformly mixed in, #10%# of the liquid we remove will be antifreeze, so we will also be removing #0.1x# litres of antifreeze. Then we will add in #x# litres of antifreeze. Thus, after the removal and addition of antifreeze, the total amount of antifreeze will be
#0.5 - 0.1x + x = 0.5 + 0.9x# litres.
Our final goal is to have the antifreeze constitute #30%# of the #5# litres of liquid, that is
#0.3*5 = 1.5# litres.
Thus, we need to drain off and replace #x# such that the total is #1.5# litres, i.e.,
#0.5 + 0.9x = 1.5#
#=> 0.9x = 1.5 - 0.5 = 1#
#=> x = 1/0.9 = 1/(9/10) = 10/9 = 1.111...#
So #10/9=1.111...# litres should be drained off.
