SOLUTION: A man is four times older than his son but five years older than his wife. The sum of their ages is 103. How old is the man?

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Question 1158671: A man is four times older than his son but five years older than his wife. The sum of their ages is 103. How old is the man?
Found 4 solutions by Edwin McCravy, Shin123, ikleyn, josgarithmetic:
Answer by Edwin McCravy(20056) About Me  (Show Source):
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A man is four times older than his son
M = 4S
but five years older than his wife.
M = W+5
The sum of their ages is 103.
M+S+W = 103
Solve this system:

system%28M=4S%2CM=W%2B5%2CM%2BS%2BW=103%29

I won't tell you the age of the man, but the son is 12.

Edwin

Answer by Shin123(626) About Me  (Show Source):
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Let the man's age be x. His son's age is x%2F4 and his wife's age is x-5. So we have the equation x%2Bx%2F4%2B%28x-5%29=103. Simplifying, we get 9x%2F4=108. Multiplying both sides by 4, we get 9x=432. Dividing both sides by 9 gives highlight%28highlight_green%28highlight%28x=48%29%29%29. Check, 48%2B48%2F4%2B%2848-5%29=48%2B12%2B43=60%2B43=highlight%28103%29.

Answer by ikleyn(52787) About Me  (Show Source):
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.

In  English,  when you use it in  Math, 
    "A man is four times older than his son"      (*)

means  this and only this 
    A man is 5 times as old as his son".


But this interpretation  (although is the  ONLY  CORRECT),  is  DEFINITELY  not that you really want,
and it leads to the non-integer answer,  which is  NONSENSE  in this kind of problems.

The cause is in that you  INCORRECTLY  use this combination of words (*).


/\/\/\/\/\/\/\/

Learn English from my posts in parallel with Math and have doubled benefits (!)



Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Assigning n for the son's age, and following the description as written:
Man         n+4n=5n
Son         n
Wife        5n-5
SUM        103

This gives equation 5n%2Bn%2B%285n-5%29=103.

11n-5=103
11n=108
n=108%2F11
n=9.818 if to three decimal figures to right of decimal point.

n, son's age is 9 years 43 weeks.
Is that the kind of result you expect?