what are the ages of a man and his son who are now now 74 and when he was his son's age now he was 99 years times his son's age then

Question

Now:  Father + son = 74

Then:  When father was the son's age now he was 99 times the son's age at that time

 

What are their ages now?

 

Answer 1

 

 There are (infinitely) many answers...

  We have three unknowns: the son's age in the past, the son's age now, and the father's age.

  

  But we have only 2 equations:  Father + son = 74;

                                                son current age = 99*son's past age

 

 For example, when the son WAS 3 months old ( 1/4 = 0.25 years), the

father was 99 times that which is 24.75. Since their current ages combine

to 74, the father is 49.25 and the son is 24.75

 

Another example is if the son WAS 0.3 years (approximately 3 months 2 weeks and a couple days)

the father was 99 times that , making him 29.7. So then the father is not 74-29.7 = 44.3

 

 

Let s be the age of the son in the past.

Then the son's current age is 99s.

The father is 74-99s

 

note that in order for the age to be positive,

74-99s>0 

74>99s

74/99>s

0.00579>s