Question 23
Suppose x,y and z are positive real numbers satisfying the following system of equations: $$\frac{\sqrt{xyz}}{x+y}=3,\qquad\frac{\sqrt{xyz}}{y+z}=\frac 52,\qquad\frac{\sqrt{xyz}}{z+x}=\frac{15}{7}.$$ If $\frac 1 x+\frac 1 y+\frac 1 z=\frac N{900}$, find N.