Question 243099
In a recent election between an incumbent and one opponent, the incumbent won by a
ratio of 7 to 6. If the opponent won 30594 votes, how many votes did the incumbent win?


Since the incubent won by a 7:6 ratio, then the incubent had 7 parts of the total votes, while the opponent had 6 parts of the total votes. Now, since the opponent's 6 parts is represented by 30,594 votes, using I as the incubent's votes, we can say that:


{{{7/6 = I/30594}}}


6I  =  7 * 30,594 --------- Cross-mutiplying


{{{I = (7*30594)/6}}}


I  =  35,693


Therefore, I, or the incubent won {{{highlight_green(35693)}}} votes.


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Check
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To check, you just need to realize that there are 13 (7 + 6) total parts, and that the incubent received {{{7/13}}} of the 66,287 (30,594 + 35,693) votes that were cast between the two candidates, while the opponent received {{{6/13}}} of the 66,287 votes that were cast between the two candidates.

_____________________________  OR  ______________________________________


we can just simply set the ratio as the incubent's votes to the opponent's votes, which is 35,693:30,594, or 7:6, or {{{35693/30594}}}, or {{{7/6}}}.