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[tex] \\ \frac{x}{ \frac{1}{3} } = \frac{y}{ \frac{1}{5} } = k \\ 3x = 5y = k \\ 3x = k = > x = \frac{k}{3} \\ 5y = k = > y = \frac{k}{5} \\ \\ x - y = 14 \\ \frac{k}{3} - \frac{k}{5} = 14 \\ \frac{5k}{15} - \frac{3k}{15} = 14 \\ \frac{2k}{15} = 14 \\ k = \frac{15 \times 14}{2} = 105 \\ \\ x = \frac{k}{3} = \frac{105}{3} = 35 \\ y = \frac{k}{5} = \frac{105}{5} = 21 \\ [/tex]
