math

A group of people was surveyed about whether the council should collect recycling once a week instead of once a fortnight. Two-thirds of the people said ‘Yes’, and one-third said ‘No’.
A year later the same group of people was surveyed again and this time one-quarter of them had changed their minds, resulting in a tie between the ‘Yes’ and ‘No’ votes.
Of the people who originally voted ‘Yes’, what fraction changed their minds?

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  1. Let x be the number who changed from No to Yes
    Let y be the number who changed from Yes to No
    If there were n people altogether, then
    1/3 n - x + y = 2/3 n - y + x
    x + y = 1/4 n
    or,
    y-x = 1/6 n
    y+x = 1/4 n
    So, y = 5/24 n
    But we want the fraction of the original Yes voters, so
    (5/24 n) / (2/3 n) = 5/16

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    oobleck

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