Vivenne, john and nassim ran for 6th grade class president. vivenne got four votes for every 3 votes that john got. nassim got two votes for every vote that vivenne got. what percentage of the votes did john get overall?

Percentage of the votes did John got overall is 25 %

Solution:

Given, Vivenne, John and nassim ran for 6th grade class president.  

Vivenne got four votes for every 3 votes that John got.  

Nassim got two votes for every vote that Vivenne got.  

Now, ratio of vivenne votes to john votes = 4 : 3

a : b can be written in fraction as

Now, ratio of nassim votes to vivenne votes = 2 : 1

Now, multiply the above two fractions,

Now, add (1) and (3),

We know that total votes = vivenne votes+nassim votes+john votes

Hence substitute "vivenne votes+nassim votes = total votes -  john votes "

Hence we get,

Multiplying 100 on both sides,

The above expression is the formula used to calculate John vote percentage

Hence John votes percentage = 25%