The table shows votes polled in a college election from 2018 to 2022, the percentage of valid votes, and the male:female ratio of valid votes. Dashes are missing values to be calculated if required.
| Year | Votes Polled | Valid (%) | Valid M:F Ratio |
|---|---|---|---|
| 2018 | — | — | 5:3 |
| 2019 | 1000 | — | 5:4 |
| 2020 | 2000 | 38 | — |
| 2021 | — | 60 | 7:5 |
| 2022 | 5000 | 40 | — |
In 2018, if the ratio of the number of valid votes was 5:4, then the number of valid votes by females in 2018 is what percent less than the number of votes polled in the same year?
The female valid votes are 70 percent less than the votes polled, so the answer is 70.
Let the votes polled in 2018 be 5x and the valid votes be 4x.
The 2018 male-to-female ratio is 5 to 3, so females are 3 of 8 parts.
So the female valid votes are 4x times 3 over 8, which is 3x over 2.
The shortfall from the votes polled is 5x minus 3x over 2, which is 7x over 2.
As a percentage of 5x this is 7x over 2 divided by 5x, times 100.
That equals 70 percent.
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