The number of votes received by winner is: 1168
Let the number of vote that is received by winning candidate be: a
and the number of votes received by other candidate be: b
It is given that:
Two candidates running for the same office received a total of 1,926 votes.
i.e.
[tex]a+b=1926--------------(1)[/tex]
and
The winning candidate had 410 more votes than the other candidate.
This means that:
[tex]a-b=410--------------(2)[/tex]
Now on solving the equation by the method of elimination .
i.e. on adding both the equation we have:
[tex]2a=1926+410\\\\i.e.\\\\2a=2336\\\\i.e.\\\\a=1168[/tex]
Now on putting the value of a in equation (1) we get:
[tex]1168+b=1926\\\\i.e.\\\\b=1926-1168\\\\i.e.\\\\b=758[/tex]
Hence, the answer is: 1168
