SOLUTION: From an original group of boys and girls, twenty girls leave. There are then left two boys for each girl. After this, sixty boys leave. There are then two girls for each boy.The nu

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Question 280051: From an original group of boys and girls, twenty girls leave. There are then left two boys for each girl. After this, sixty boys leave. There are then two girls for each boy.The number of girls in the original group was:
(A) 81 (B) 72 (C) 68 (D) 60 (E) 50
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let g = original number of girls
Let b = original number of boys
given:
Initially, there are:
b+%2B+g in the group
20 girls leave
b+%2B+%28g+-+20%29 in the group
(1) b+=+2%2A%28g+-+20%29
Then 60 boys leave
%28b+-+60%29+%2B+%28g+-+20%29 in the group
(2) g+-+20+=+2%2A%28b+-+60%29
(1) and (2) are 2 equations with 2 unknowns, so
it's solvable
(1) b+=+2%2A%28g+-+20%29
(1) b+=+2g+-+40
(1) 2g+-+b+=+40
(2) g+-+20+=+2%2A%28b+-+60%29
(2) g+-+20+=+2b+-+120
(2) -g+%2B+2b+=+100
Multiply both sides of (1) by 2 and add equations
(1) 4g+-+2b+=+80
(2) -g+%2B+2b+=+100
3g+=+180
g+=+60
The number of girls in the original group was 60
check answer:
(1) b+=+2%2A%28g+-+20%29
b+=+2%2A%2860+-+20%29
b+=+80
(2) g+-+20+=+2%2A%28b+-+60%29
(2) 60+-+20+=+2%2A%2880+-+60%29
40+=+2%2A20
40+=+40
OK