Last year, all registered voters in Kumania voted either for the Revolutionary Party or the Status Quo Party. This year, the number of Revolutionary voters increased 10%, while the number of Status Quo voters increased 5%. No other votes were cast. If the number of total voters increased 8%, what fraction of voters voted Revolutionary this year?
Let's assume that of the registered voters in Kumania, x voted for the Revolutionary party while y voted for the Status QUO party. If this is the case, then this year there were:
1.10x Revolutionary voters and 1.05y Status QUO voters. If the total number of voters this year was an 8% from last year's, then:
1.08(x+y)=1.10x+1.05y
3y=2x
We're looking for 1.10x/1.10x+1.05y. Substitute x=3/2y into the expression to get:
1.10(3/2y)=33/20y
33/20y/(33/20y+21/20y)=33/20y/(54/20y)=33/54=11/18.
