A school had an election where the candidates received votes in the ratio of 1:2:3. If the winning candidate received 210 votes, how many people voted in the election?

Accepted Solution

now, let's say the total of folks voting were "x".

now, if we divide "x" even into "1+2+3" pieces, we'd get some quotient value, the first candidate took 1 of those even pieces, the second candidate took 2 of those even pieces, and the winning candidate took 3 of them, thus winning anyway.

let's do the division, keeping in mind that the winning candidate had 210 votes.

[tex]\bf \cfrac{x}{1+2+3}\implies \cfrac{x}{6}\implies \stackrel{\textit{winning candidate pieces}}{3\cdot \cfrac{x}{6}}=\stackrel{\textit{winning candidate votes}}{210} \\\\\\ \cfrac{3x}{6}=210\implies \cfrac{x}{2}=210\implies x=420[/tex]