$$1 : m = 3 : 5 m : n = 6 : 7 1 : n$$
$\frac{1}{m}=\frac{3m}{5n}\text{ and }\frac{3m}{5n}=\frac{6}{7n}$
$n = \frac{60}{49} = 1\frac{11}{49} \approx 1.224489796$
$m = \frac{10}{7} = 1\frac{3}{7} = 1.4285714285714286$
$m = \frac{10}{7} = 1\frac{3}{7} = 1.4285714285714286$
$n = \frac{60}{49} = 1\frac{11}{49} = 1.2244897959183674$
