SOLUTION: From a group of boys and girls, 15 girls leave. There are then left two boys for each girl. After 45 boys leave, there are then 5 girls for each boy. The number of girls in the beg

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Question 279669: From a group of boys and girls, 15 girls leave. There are then left two boys for each girl. After 45 boys leave, there are then 5 girls for each boy. The number of girls in the beginning was:
(A) 40 (B) 43 (C) 29 (D) 50 (E) 60
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let b = number of boys in the beginning
Let g = number of girls in the beginning
15 girls leave, so
b+%2B+%28g+-+15%29 in the group
There are 2 boys for each girl, so
b+=+2%2A%28g+-+15%29
45 boys leave, so
%28b+-+45%29+%2B+%28g+-+15%29 in the group
Now there are 5 girls for each boy, so
g+-+15+=+5%2A%28b+-+45%29
g+-+15+=+5b+-+225
5b+=+g+%2B+210
b+=+%28g+%2B+210%29%2F5
I'll substitute this into b+=+2%2A%28g+-+15%29
%28g+%2B+210%29%2F5+=+2g+-+30
g+%2B+210+=+10g+-+150
9g+=+360
g+=+40
There were 40 girls in the beginning- (A)
check:
b+=+2%2A%28g+-+15%29
b+=+2%2A%2840+-+15%29
b+=+2%2A25
b+=+50 and g+=+40 in the original group
15 girls leave, so
b+=+50, g+=+25
There are 2 boys for each girl- that checks
45 boys leave, so
b+=+5, g+=+25
There are 5 girls for each boy- OK