SOLUTION: a girl is half as old as her brother and two years younger than her sister. The sum of the ages of the three children is 34 years. How old is each child?

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Question 5246: a girl is half as old as her brother and two years younger than her sister. The sum of the ages of the three children is 34 years. How old is each child?
Answer by longjonsilver(2297) (Show Source):
You can put this solution on YOUR website!
Let age of girl = x
Let age of brother = y
Let age of sister = z
x = y/2 --> 2x = y --> 2x - y = 0 --eqn1
x = z-2 --> z = x+2 --eqn2
x+y+z = 34 --eqn3

Sub eqn2 into 3, to give x+y+x+2 = 34
--> 2x+y = 32 --eqn4

So, we now have 2 equations to use: eqn1 and eqn4.
2x - y = 0
2x + y = 32

Subtracting these gives

-2y = -32
y = 16

so, as x=y/2 --> x=16/2 --> x=8
and z = x+2, so z = 10

So ages are: girl=8, brother=16 and sister=10

jon.