SOLUTION: 40% of the population of a town are men and 39% are women. If the number of children is 1260. Find the number of men. (Ans.2400)

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Question 498793: 40% of the population of a town are men and 39% are women. If the number of children is 1260. Find the number of men. (Ans.2400)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There can only be men, women, or children, so
Let m = number of men
Let w = number of women
given:
(1) +m+%2B+w+%2B+1260+ = population
(2) +m+=+.4%2A%28+m+%2B+w+%2B+1260+%29+
(3) +w+=+.39%2A%28+m+%2B+w+%2B+1260+%29+
---------------------------
(2) +m+=+.4m+%2B+.4w+%2B+504+
(2) +.6m+-+.4w+=+504+
(2) +60m+-+40w+=+50400+
and
(1) +w+=+.39m+%2B+.39w+%2B+491.4+
(1) -.39m+%2B+.61w++=++491.4+
(1) +-39m+%2B+61w+=+49140+
-------------------------
Add the equations
(2) +60m+-+40w+=+50400+
(1) +-39m+%2B+61w+=+49140+
+21m+%2B+21w+=+99540+
+21%2A%28+m+%2B+w+%29+=+99540+
+m+%2B+w+=+4740+
and, since
+m+%2B+w+%2B+1260+ = population
+4740+%2B+1260+=+6000+ = population
Going back to (2)
(2) +m+=+.4%2A%28+m+%2B+w+%2B+1260+%29+
(2) +m+=+.4%2A6000+
(2) +m+=+2400+
There are 2400 men
check the answer:
(3) +w+=+.39%2A%28+m+%2B+w+%2B+1260+%29+
(3) +w+=+.39%2A6000+
(3) +w+=+2340+
and
(1) +m+%2B+w+%2B+1260+ = 6000
(1) +2400+%2B+2340+%2B+1260+=+6000+
(1) +6000+=+6000+
OK