The population of a village is 6400.
Let M = the ORIGINAL number of males in the village
Let F= the ORIGINAL number of females in the village
So, we can write: M + F = 6400

If the number of males increased by 40% and that of females increased by 30%, the population becomes 8380.
So, 1.4M = the RESULTING number of males
And 1.3F = the RESULTING number of females
So, we can write: 1.4M + 1.3F = 8380

What is the population of females in the town?
We now have the following system of equations:
M + F = 6400
1.4M + 1.3F = 8380

Take the top equation, and multiply both sides by 1.4 to get the following equivalent equation:
1.4M + 1.4F = 8960
1.4M + 1.3F = 8380

Now subtract at the bottom equation from the top equation to get: 0.1F = 580
Solve: F = 580/0.1 = 5800

Answer: D
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