When 2/9 of the votes on a certain resolution have been counted, 3/4 of thoes counted are in favor of the resolution. What fraction of the remaining votes must be against the resolution so that the total count will result in a vote of 2 to 1 against the resolution?
If we use variable for total votes there will be too many fractions to manipulate with, so pick some smart #: let set total # of votes is 18.
"2/9 of the votes on a certain resolution have been counted" --> 4 counted and 18-4=14 votes left to be counted;
"3/4 of those counted are in favor of the resolution" --> 3 in favor and 1 against;
Ratio of those who voted against to those who voted for to be 2 to 1 there should be total of 18*2/3=12 people who voted against, so in the remaining 14 votes there should be 12-1=11 people who voted against. Thus 11/14 of the remaining votes must be against.
Did in the same way, just created a table as below