In an election for a representative on school council, there were only two candidates.
Sophia received \(60\%\) of the total votes and Mireille received all the rest. If Sophia won by \(28\) votes, then how many people voted?
Solution 1
If Sophia received \(60\%\) of the votes, then Mireille received \(40\%\) of the total number of votes. The difference between them, \(20\%\), represents \(28\) votes.
We are interested in determining \(100\%\) of the votes, that is, the total number of votes cast. Since we know that \(20\%\) of the total votes cast was \(28\) votes and \(5\times 20=100\), then a total of \(5\times 28\) or \(140\) people voted.
Solution 2
The second solution uses an algebraic approach.
Let \(n\) represent the total number of votes cast.
Since Sophia received \(60\%\) of the total votes, she received \(0.6\times n\) or \(0.6n\) votes.
Since Mireille received all of the remaining votes, she received \(0.4\times n\) or \(0.4n\) votes.
The difference between the number of votes received by Sophia and the number of votes received by Mireille was \(28\). So, \[\begin{aligned} 0.6n -0.4n &= 28 \\ 0.2n &= 28\\[1mm] \frac{0.2n}{0.2}&=\frac{28}{0.2}\\[1mm] n &= 140 \end{aligned}\] Therefore, \(140\) people voted.