SOLUTION: From a group of boys and girls, 14 girls leave first. Then the ratio of the number of girls to the number of boys becomes 1:2. After this, 43 boys leave the group. Now the boys and

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Question 826543: From a group of boys and girls, 14 girls leave first. Then the ratio of the number of girls to the number of boys becomes 1:2. After this, 43 boys leave the group. Now the boys and girls are equal in number. How many girls were there in the beginning?
Answer by ankor@dixie-net.com(22740) (Show Source):
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From a group of boys and girls, 14 girls leave first.
Then the ratio of the number of girls to the number of boys becomes 1:2.
After this, 43 boys leave the group.
Now the boys and girls are equal in number.
How many girls were there in the beginning?
:
Let g = no. of girls originally
let b = no. of boys originally
:
"From a group of boys and girls, 14 girls leave first.
Then the ratio of the number of girls to the number of boys becomes 1:2.
=
Cross multiply
1b = 2(g-14)
b = 2g - 28
:
" After this, 43 boys leave the group.
Now the boys and girls are equal in number."
b - 43 = g - 14
b = g - 14 + 43
b = g + 29
Replace b with (2g-28)
2g - 28 = g + 29
2g - g = 29 + 28
g = 57 girls originally
:
:
We can confirm this by finding the no. of boys
b = 2(57) - 28
b = 86 boys
= =