Henry Ernest Dudeney/Modern Puzzles/83 - A Critical Vote/Solution

by : $83$

 * A Critical Vote

Solution
There were $207$ people at the meeting, of which $103$ voted in favour and $104$ against.

Proof
Let $n$ be the total number of people at the meeting.

Let $a$ be the number of people in favour of the motion.

Let $b$ be the number of people against the motion.

Let $m$ be the number of people who wanted to vote against the motion but could not, as they could not sit down.

We have: