Five people ran for President of a local town board, how many votes did the winner receive?

Question

Five people ran for President of a local town board. A total of 1678 people voted. The winner had 101 more votes than 1 candidate, 130 votes more than a second candidate, 157 votes more than another candidate and 204 votes more than the last candidate. How many votes did the winner receive?

Answer 1

Let W = winner's total.  Then W  + (W - 101) + (W-130) + (W -  157) + (W - 204)  = 1678

 

Combining:  5 W - 592  = 1678

Then  5W = 1678 + 592 = 2270

 

Thus   W  = 2270/5 = 454 votes