Alternative method that's not described in the solution is the backsolving. Take a look at the answer choices:

* 21

* 24

* 36

* 42

* 45

The problem states that the final ratio was 3:4 - that means that our answer choice has to be a multiple of 7. Only 2 answer choices fall into that category - A and D.

Backsolving for those yields:

A: 21 total employees or 9 female and 12 male. If we subtract 3 male, the ratio will be 50/50. Wrong.

D: 42 total employees or 18 female and 24 male. If we subtract 3 male, that's 18:21 or 6:7 - match

Hopefully this helps a little - this is probably the most elegant solution but you need to get comfortable with these.

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