The compounded ratio of two ratios [tex]a\div b[/tex] and [tex]c\div d[/tex] is defined as [tex]ac\div bd[/tex].
So, in your case, we have
[tex]\dfrac{7\cdot 8}{5x}=\dfrac{83}{60}[/tex]
Solving for [tex]x[/tex] yields
[tex]x=\dfrac{56\cdot 60}{5\cdot 83}=\dfrac{672}{83}[/tex]
