SOLUTION: The sum of the present ages of the father and son is 60 years old. 6 years ago, the father is 5 times as old as the son. What are their ages 6 years from now?

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Question 853790: The sum of the present ages of the father and son is 60 years old. 6 years ago, the father is 5 times as old as the son. What are their ages 6 years from now?
Found 2 solutions by Edwin McCravy, dkppathak:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!


The sum of the present ages of the father and son is 60 years old. 
F+S = 60

6 years ago, the father was 5 times as old as the son. 
F-6 = 5(S-5)

System of equations:

F+S = 60
F-6 = 5(S-5)

Solve the first for F

F+S = 60
  F = 60-S

Substitute (60-S) for F in the second equation:

     F-6 = 5(S-5)
(60-S)-6 = 5(S-6)

Remove parentheses

 60-S-6 = 5S-30
   54-S = 5S-30
     84 = 6S
     14 = S

Substitute 14 for S in 

      F = 60-S
      F = 60-14
      F = 46

What are their ages 6 years from now?
The father if 46.  6 years from now he will be 52.
The son is 14.  6 years from now he will be 20.

Edwin
Answer by dkppathak(439)   (Show Source): You can put this solution on YOUR website!
The sum of the present ages of the father and son is 60 years old. 6 years ago, the father is 5 times as old as the son. What are their ages 6 years from now?
let present age of son is s yrs and father age is f yrs
as per given conditions
s+f=60 (1)
f=60-s
6 yrs ago age of son is s-6
and father age 6 yrs ago father was=60-s-6
father age was =54-s
as per given conditions father is 5 times of son
54-s=5(s-6)
54=5s-30+s
6s=54+30
s=84/6=14
present age of son is 14 yrs father is 60-s=60-14=46 yrs
6 yrs from now age of son will be s+6=14+6=20 yrs
age of father 6 yrs from now =F+6=46+6=52 yrs
Answer
son age 6 yrs from now =20 yrs
and father =52 yrs

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