A father's age is 4 times that of his son. 5 years ago, the age of the father was 7 times that of his son. What is the present age of father and his son?

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Answer 1 · 2017-08-11T07:28:22

The son is 10 yo. and the father is 40 yo.

So the father's age (F) is 4 times the son's age (S).

#F = 4 xx S#

5 years ago, the father's age (#F-5#) was 7 times that of his son 5 years ago (#S-5#).

#F-5=7 xx (S-5)#

So:

#F=7 xx (S-5) +5larr# adding 5 to both sides

Now we can take the first equation and set it equal to the second, since both "right" sides are equal to F.

#7xx(S-5) +5 = 4xxS#

Now we solve for S:

#7xxS-7xx5+5 = 4xxSlarr#distributing the 7

#7xxS-35 + 5 = 4xxSlarr#finishing the multiplication

#7xxS-30 = 4xxSlarr# adding #-30# and #5#

#7xxS=4xxS+30larr#adding 30 to both sides

#7xxS-4xxS=30larr#subtracting #4xxS# from both sides

#3xxS=30larr#subtracting #4xxS# from #7xxS#

#S=30/3larr#dividing both sides by 3

#S=10#

So, the son's current age is 10 years old and the fathers is 4 times that, or 40 years old.