SOLUTION: Please answer this..ASAP.Thanks..a man is four years older than his wife and 5 times as old as his son.when the so was born,the age of the wife is six-seventh that of her husband's
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Question 517559: Please answer this..ASAP.Thanks..a man is four years older than his wife and 5 times as old as his son.when the so was born,the age of the wife is six-seventh that of her husband's age. Find the age of the wife..
Found 2 solutions by Maths68, MathTherapy:
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
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
------------
5s-w-4=0................(4)
Multiply (2) by 6 and add to (3)
6m-30s=0
7w-s-6m=0
---------------
7w-31s=0............(5)
Multiply (4) by 7 and add to (5)
7w-31s=0............(5)
35s-7w-28=0
--------------
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
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Age_Word_Problems/517559: Please answer this..ASAP.Thanks..a man is four years older than his wife and 5 times as old as his son.when the so was born,the age of the wife is six-seventh that of her husband's age. Find the age of the wife..
1 solutions
Let wife’s age be W
Then man’s age = W + 4
S, or son’s age = man’s age, or , or
35W – 7(W + 4) = 6(5W + 20 – W – 4) -------- Multiplying by LCD, 35
35W – 7W – 28 = 30W + 120 – 6W – 24
28W – 24W = 96 + 28
4W = 124
W, or wife’s age = , or
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