More about discovering ages

The solution is the following:

AGES TWO PEOPLE THERE WERE 8 YEARS IN REASON OF 8 TO 11; NOW IS THE REASON OF 4 TO 5. WHAT IS THE AGE OLDER CURRENTLY?

We call y the age of the youngest person.

We call it x age of the older person.

The problem is that now (currently) ages are in the ratio of 4 to 5. Then:

y / x = 4/5 (equation 1)

The problem is that for 8 years ages were in the ratio of 8 to 11. So:

(8-y) / (x-8) = 8/11 (Equation 2)

Isolating y in equation 1:

4x = y / 5

Putting this value of y in equation 2 we have:

((4x / 5) -8) / (x-8) = 8/11

(4x / 5) = 8/11 -8. (X-8)

Making mmc on both sides we have:

(4x-40) / 5 = (8x-64) / 11

11. (4x-40) = 5 (8x-64)

440 = 44x-40x-320

44x-40x = 440-320

4x = 120

x = 30

So the age of the oldest person is 30 years !!!