Question 923594: Eight years ago there were 5 members in
arthur's family and then average age of family
was 36. Meanwhile arthur got married and gave
birth to child. Still average age remains
constant. what was the age of his wife at the
time of his child's birth If the difference
between age of her child and herself is 26
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if their average age 8 years ago was 36, then their average age today is 44.
their total age 8 years ago was 36 * 5 = 180
their total age today is 44 * 5 = 220
the family added a wife and a child.
if the average age is still 36, then you get 7*36 = 252
their total age today should be equal to 252 because 252 / 7 = 36
so, without the woman and child, their total age today is 220.
with the woman and child, their total age is 252.
the woman and child add 32 to the total age.
assuming the woman is y years old and the child is y - 26 years old, then you get:
2y - 26 = 32
solve for y to get:
y = 29
the woman must be 29 years old and the child must be 3.
let's see if that works.
8 years ago their average age was 36 for a total of 5 * 36 = 180 years.
their total age without the woman and child is equal to 36 + 8 = 44 * 5 = 220 years today.
add 29 for the woman and 3 for the child and you get a total of 252 years.
divide that by 7 and you get an average of 36
numbers look good so the solution appears to be:
age of the woman is 29.
age of the child is 3.
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