Question 891808
Let x = one number, so that 50 - x = the other number.

Then {{{(50-x)/15 = 15/x}}}
==> {{{50x - x^2 = 225}}}
==> {{{0 = x^2 - 50x + 225}}}
<==> (x-5)(x-45) = 0
Thus the numbers are 5 and 45.