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