The solution is as follows:
We will call y the age of the youngest person.
We will call x the age of the oldest person.
The problem is that now (currently) the ages are in the 4 to 5 ratio. So:
y / x = 4/5 (equation 1)
The problem is that 8 years ago the ages were in the ratio of 8 to 11. So:
(y-8) / (x-8) = 8/11 (equation 2)
Isolating y in equation 1:
y = 4x / 5
Putting this value of y in equation 2 we have:
((4x / 5) -8) / (x-8) = 8/11
(4x / 5) -8 = 8/11. (X-8)
Making the mmc on both sides we have:
(4x-40) / 5 = (8x-64) / 11
11. (4x-40) = 5. (8x-64)
44x-440 = 40x-320
44x-40x = 440-320
4x = 120
x = 30
So the age of the oldest person is 30 years old !!!
Back to the statement