The population of a town is 6000. If the number of males increases by 10% and the number of females increases by 20%, then the population becomes 6800. Find the population of females in the town.
Question
The population of a town is 6000. If the number of males increases by 10% and the number of females increases by 20%, then the population becomes 6800. Find the population of females in the town.
Solution
Let's denote the number of males in the town as M and the number of females as F. We know from the problem that:
M + F = 6000 (equation 1)
After the increase, the number of males is M + 0.10M = 1.10M and the number of females is F + 0.20F = 1.20F. The total population after the increase is:
1.10M + 1.20F = 6800 (equation 2)
We can solve these two equations to find the values of M and F. Let's multiply equation 1 by 1.10:
1.10M + 1.10F = 6600 (equation 3)
Now, let's subtract equation 3 from equation 2:
1.20F - 1.10F = 6800 - 6600
0.10F = 200
So, F = 200 / 0.10 = 2000
Therefore, the population of females in the town is 2000.
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