Question 625087
Let
Present age of the girl=g years old
Present age of the brother=b years old
Present age of the sister=s years old


Girl is half as old as her brother
g=b/2
2g=b
b=2g.............(1)
and two years younger than her sister
g=s-2
g-s=-2.............(2)
The sum of the age of the three children is 34 years
g+b+s=34..........(3)
Put the value of b from (1) to (3)
g+b+s=34
g+2g+s=34
3g+s=34............(4)
Multiply (2) by -3 and add to (4)
3g+s=34
-3g+3s=6
---------------
4s=40
Divide by 4 both sides of the above equation
4s/4=40/4
s=10
Put the value of s in (2)
g-s=-2.............(2)
g-10=-2
g=-2+10
g=8
Put the value of g in (1)
b=2g.............(1)
b=2(8)
b=16


Present age of the girl=g=8 years old
Present age of the brother=b=16 years old
Present age of the sister=s=10 years old