A man is 4 times as old as his son. In 3 years, the father will be 3 times as old as his son. How old is each of them now?

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Assume that the son's age = x

then the man age = 4 times as old ad his son = 4x

after 3 years:

the son age = x+3

the man age = 3 times as old as his son = 3(X+3)

but 3 years later, the man age was...

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Assume that the son's age = x

then the man age = 4 times as old ad his son = 4x

after 3 years:

the son age = x+3

the man age = 3 times as old as his son = 3(X+3)

but 3 years later, the man age was 4x so now his age is 4x+3

then 3(x+3) = 4x +3

==> 3x+9 = 4x +3

==> 6 = x

then the son age now = 6

and the man age = 4(6) = 24

after 3 years, the son will be 9

and the father will be 24+3 = 27 or 3(9)= 27

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Right now, the man is 24 and his son is 6.  Here is how you figure this out:

Let the man's age by M and the son's age be S.

Right now M = 4S

In three years

M + 3 = 3(S + 3)

So you put the 4S in to substitute for the M.

4S + 3 = 3(S + 3)

4S + 3 = 3S + 9

S = 6

If the son is 6, the father must be 24.

We can check this by adding three to both ages. Then, the son will be 9 and the father will be 27, which is three times 9.

 

 

Approved by eNotes Editorial Team