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[tex] \bf \dfrac{x}{y} = \dfrac{7}{10} \implies \: x = \dfrac{7}{10} \cdot y[/tex]
[tex] \bf \dfrac{3x + 4y}{5x + 2y} = \dfrac{3\dfrac{7y}{10} + 4y}{5\dfrac{7y}{10} + 2y} = \dfrac{\dfrac{21y}{10} + 4y}{\dfrac{35y}{10} + 2y}[/tex]
[tex] \bf \dfrac{\dfrac{21y + 40y}{10}}{\dfrac{35y + 20y}{10}} = \dfrac{\dfrac{61y}{10}}{\dfrac{55y}{10}} = \dfrac{61y}{10} \cdot \dfrac{10}{55y} = \dfrac{61y}{ \not10} \cdot \dfrac{ \not10}{55y} = \dfrac{61}{55} [/tex]
[tex]\boxed {\bf \dfrac{61}{55} }[/tex]