In this task, you need to answer the given multiple-choice question on the general math. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.

Problem: if 2 ^ ( 2 w ) = 8 ^ ( w − 3 ) , what is the value of w ? 
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
c

Problem: there are two numbers . if 20 % of the first number is added to the second number , then the second number increases to its 5 - fourth . what is the ratio of the first number to the second number ? 
Options: a ) 2 : 9 , b ) 3 : 8 , c ) 8 : 5 , d ) 5 : 4 , e ) 7 : 3
d

Problem: when 2 / 9 of the votes on a certain resolution have been counted , 3 / 4 of those counted are in favor of the resolution . what fraction w 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 ? 
Options: a ) 11 / 14 , b ) 13 / 18 , c ) 4 / 7 , d ) 3 / 7 , e ) 3 / 14

a