# The average age of three women is increased by 4kg. When one of them who's weight is 100 kg is replaced by another woman. What is the weight of the new women?

Let the average weight of 3 women be x,

then the Sum of the weight of 3 women =3 x
If a woman is replaced, then the average weight of 3 women =(x+4)
If a woman is replaced, then sum of weight of 3 women =3(x+4)=3x+12
Let weight of new woman be y, then
According to the question
\begin{aligned} &3x-100+y=3x+12 \\ &\Rightarrow y=3x+12+100-3x \\ &\therefore y=112 \end{aligned}

So the weight of the new woman is 112 kg

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