SOLUTION: when the son will be as old as father there ages will add up to 126 years. when the father was as old as the son in today there ages added up to 38 years. find their present age

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Question 1040377: when the son will be as old as father there ages will add up to 126 years. when the father was as old as the son in today there ages added up to 38 years. find their present age
Answer by ikleyn(52788) About Me  (Show Source):
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When the son will be as old as father their ages will add up to 126 years.
When the father was as old as the son in today there ages added up to 38 years. Find their present age.
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Let "s" be the son's present age.
Let "f" be the father's present age.

When the son will be as old as the father is now? - In f-s years.
At that time the son will be f years old and the father will be f + (f-s) = 2f-s years old.

Their ages added up at that time will be f + (2f-s) = 3f-s years.
It gives you the first equation 

3f - s = 126.    (1)


When the father was as old as the son is now? - In f-s years.
At that time the father's age was s years old and the son's age was s - (f-s) = 2s-f years old  (assuming that 2s-f >= 0).

Their ages added up at that time were s + (2s-f) = 3s-f years.
It gives you the second equation 

3s - f = 38.     (2)

Now express s from (1): s = 3f - 126,  and substitute it into (2). You will get

3(3f-126) - f = 38,   or

9f - 378 - f = 38,

8f = 38 + 378 = 416.

Hence, f = 416%2F8 = 52.

Father's current age is 52 years.

Then the sun's age is s = 3f - 126 = 30.   (notice that the intermediate assumption 2s - f >= 0 is valid !)

Solved.

For age word problems see the lessons
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    - Age problem for the day of April, 1
    - OVERVIEW of lessons on age problems
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