Explanation:
I think you made a typo.
the son can never have been older than his father.
so, the ratio of their ages 8 years ago must have been 14:13.
x = father's age now
y = son's age now
x/y = 5/2
x = 5y/2
(x-8)/(y-8) = 14/13
(5y/2 - 8)/(y - 8) = 14/13
5y/2 - 8 = 14(y - 8)/13
5y - 16 = 28(y - 8)/13
65y - 208 = 28y - 224
37y = -16
y = -16/37
a negative age. something is wrong with the numbers in the question. there must be an additional typo.
although it does not make sense, I try now also the 13/14 ratio from 8 years ago :
(5y/2 - 8)/(y - 8) = 13/14
5y/2 - 8 = 13(y - 8)/14
5y - 16 = 26(y - 8)/14
70y - 224 = 26y - 208
44y = 16
y = 16/44 = 4/11 = 0.363636363... years old.
note the age is at least positive, but still dies not make any sense, as 8 year ago this would have still been a negative age.
what could the right numbers have been ?
basing on the current 5/2 ratio, that could mean e.g the father is 40, and the son is 16.
8 years ago that would have been 32/8 = 4/1.
or 50/20 now, 42/12 = 7/2 8 years ago.
or 60/24 now. 52/16 = 13/4 8 years ago. that might be the typo
let's therefore assume the ratio 8 years ago was 13/4.
(5y/2 - 8)/(y - 8) = 13/4
5y/2 - 8 = 13(y - 8)/4
5y - 16 = 26(y - 8)/4
20y - 64 = 26y - 208
144 = 6y
y = 144/6 = 24 years old now.
x = 5y/2 = 5×24/2 = 4×12 = 60 years old now.
so, I believe, the father is now 60 years old the son is now 24 years old.
please pay more attention to copying the right info (numbers, operation symbols, ...). we are not psychics here. although you can see, we are trying very much to be ...