SOLUTION: A man is 4 years older than his wife and 5 times as old as his son.When the son was born,the age of the wife is six-seventh that of her husband's age.Find the age of his wife.

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Question 516307: A man is 4 years older than his wife and 5 times as old as his son.When the son was born,the age of the wife is six-seventh that of her husband's age.Find the age of his wife.
Answer by Maths68(1474) (Show Source):
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Let
Present age of Man = m
Present age of Wife = w
Present age of Son = s
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Man is 4 years older than his wife
m=w+4
m-w-4=0...........(1)
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5 times as old as his son.
m=5s
m-5s=0............(2)
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Age of the man when son was born means that we have to subtract age of Son from the age of Man and age of wife so the age of the man was (m-s) and age of wife (w-s) then the age of the wife is six-seventh that of her husband's age.
w-s=6/7(m-s)
7(w-s)=6(m-s)
7w-7s=6m-6s
7w-7s-6m+6s=0
7w-s-6m=0...........(3)
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We have three equations and three unkowns (m,w,s)
m-w-4=0...........(1)
m-5s=0............(2)
7w-s-6m=0...........(3)
Subtract (2) from (1)
m-w-4=0
-m+5s=0
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5s-w-4=0................(4)
Multiply (2) by 6 and add to (3)
6m-30s=0
7w-s-6m=0
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7w-31s=0............(5)
Multiply (4) by 7 and add to (5)
7w-31s=0............(5)
35s-7w-28=0
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4s-28=0
4s=28
4s/4=28/4
s=7
Put the value of s in (2)
m-5s=0............(2)
m-5(7)=0
m-35=0
m=35
Put the value of m in (1)
m-w-4=0...........(1)
35-w-4=0
-w+31=0
-w=-31
w=31
Present age of Man = m = 35 years old
Present age of Wife = w = 31 years old
Present age of Son = s = 7 years old