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 246298: 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 ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
From a group of boys and girls,
b = no. of boys
g = no. of girls
:
then 15 girls leave. There are then left two boys for each girl.
b%2F%28g-15%29 = 2%2F1
Cross multiply
b = 2(g-15)
b = 2g - 30
:
After 45 boys leave, there are then 5 girls for each boy.
%28b-45%29%2F%28g-15%29 = 1%2F5
Cross multiply
g-15 = 5(b-45)
g - 15 = 5b - 225
g = 5b - 225 + 15
g = 5b - 210
:
The number of girls in the beginning was:
Replace b in the above equation with (2g-30) from the 1st equation:
g = 5(2g-30) - 210
g = 10g - 150 - 210
g = 10g - 360
g - 10g = -360
-9g = -360
g = %28-360%29%2F%28-9%29
g = +40 girls originally