word problem

Question

from a group of boys and girls. 15 girls leave there are then left 2 boys for each girl. after this 45 boys leave. there are then 5 girls for each boy find the number of girls in the beginning 

 

 

please give me detail answer

Answer 1

Start by assigning variables...  Let g = the original number of girls and let b = the original number of boys.

 

After 15 girls leave, there are g - 15 girls left.  If there are 2 boys for each girl at that point, then b = 2(g - 15).

 

Then 45 boys leave, so there are b - 45 boys.  At that point, the number of girls (still g - 15) is 5 times the number of boys (b - 45), so g - 15 = 5(b - 45)

 

So we have two equations to solve together:

 

b = 2(g - 15)

g - 15 = 5(b - 45)

 

First simplify:

 

b = 2g - 30

 

g - 15 = 5b - 225

g = 5b - 210

 

Since the first equation is an expression for b in terms of g, you can use substitution in the second equation:

 

g = 5b - 210

g = 5(2g - 30) - 210

g = 10g - 150 - 210

g = 10g - 360

-9g = -360

g = 40

 

Since b = 2g - 30, b = 2(40) - 30 = 80 - 30 = 50

 

So the original number of girls was 40, and the original number of boys was 50.