Call the amount Paul as have x, Helen as have y.
x + y = 90
(y + 16) - (x - 16) = 14 [ y + 16 = helen receives 16, x - 16 = paul lose 16, (y+16) - (x-16) = 14 -> the difference between their money at that moment is 14. ]
Break bracket : y + 16 - x + 16 = 14
y - x + 32 = 14
y - x = -18
-> x - y = 18
So, x + y = 90, x - y = 18
-> x = (90+18)/2 = 54
y = 90 - 54 = 36
Recheck :
When Paul gives Helen 16, then Paul has 54 - 16 = 38
Helen has 36 + 16 = 52
That is 14 less, so it satisfies the question.
