SOLUTION: Hi in 2002 the ratio of male teachers to female teachers was 4:5 in 2004 there were 2400 new teachers and the ratio of male to female became 8:9.how many teachers were there in 20

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Question 1014046: Hi
in 2002 the ratio of male teachers to female teachers was 4:5 in 2004 there were 2400 new teachers and the ratio of male to female became 8:9.how many teachers were there in 2002.
thanks
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
The ratio in 2002 was 4/5 or 4x/5x.
Assuming that the 2400 new teachers were half women and half men, we can write
%284x%2B1200%29%2F%285x%2B1200%29+=+8%2F9
Cross-multiplying we get
9(4x+1200) = 8(5x+1200)
36x + 10800 = 40x + 9600
1200 = 4x
x = 300
which means that originally there were
4(300) = 1200 male teachers and
5(300) = 1500 female teachers...
2700 total teachers in 2002...