Mathland election
A political commentator summed up an election result. Given that there were just four candidates and that the figures quoted were exact find the number of votes polled for each candidate.
Age
11 to 14
Challenge level
Problem
On Mathland TV a political commentator summed up an election result as follows.
A Labour majority of $1729$ last time has been turned into a Conservative majority of $1654$ in this election and the conservative candidate has obtained $38\%$ of the poll. Labour has taken second place. The Liberal Democrat has obtained only $14\%$ of the poll and has been beaten into fourth place by the SNP candidate who has $50$ more votes than the Liberal Democrat.
Given that there were just four candidates and that the figures quoted were exact find the number of votes polled for each candidate.
[This question comes from the book 'Mathematical Challenges' published in 1989 for the Scottish Mathematical Council by Blackie, ISBN 0216 92622X]
Student Solutions
We have received correct solutions from Sarah Dunn, Ben Falconer, Fern Smith and Ian Downie, all from Madras College. Well done to you all.
They all used a similar argument:
| Conservative | $38\%$ |
|---|---|
| Labour | $38\% - 1654$ votes |
| SNP | $14\% + 50$ votes |
| Liberal Democrat | $14%$ |
Since all the votes add up to 100%
$38\% + 38\% -1654 +14\% + 50 + 14\% = 100\%$
$104\% - 1604 = 100%$
therefore $4\% = 1604$ votes
$1\% = 401$ votes
and $100\% = 40100$ total votes.
Therefore
| Conservative | $38\%$ of $40100 =$ | $15238$ votes |
|---|---|---|
| Labour | $15238 - 1654 =$ | $13584$ votes |
| SNP | $5614 + 50 =$ | $5664$ votes |
| Liberal Democrat | $14% of 40100 =$ | $5614$ votes |
| TOTAL | $40100$ votes |