in a local election,138,201 people voted for the winning candidate.ifshe won by 29,288 votes,about how many votes did the other candidate recive

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Answer: 108,913 people vote for other candidates

In this case, you know the total number of winning voters and the vote differences between two candidates. Then the Winning (W) and Losing(L) candidate equation would be :
W= 138,201
W-L = 29,288 

If you put the first equation into the second, you will get
W-L = 29,288 
138,201-L= 29,288 
-L= 29,288 - 138,201
-L= -108,913
L= 108,913