Problem:
From a group of boys and girls, 15 girls leave. There are then left two boys for each girl. After this 45 boys leave. There are then 5 girls for each boy. The number of girls in the beginning was:
Answer Choices:
A. 40
B. 43
C. 29
D. 50
E. none of these
Solution:
If B is the original number of boys and G the original number of girls, then
B=2(G−15)
Substituting into G−15B−45=51 gives:
G−152(G−15)−455(2(G−15)−45)5(2G−30−45)5(2G−75)10G−3759GG∴G=51=G−15=G−15=G−15=G−15=360=9360=40