Question

If $x$ varies directly with $3y+5$ and $y=\frac{3}{5}$ when $x=10$, then what is the value of $y$ when $x=35$?

Answer 1

$x$ Varies directly with $3y+5$

i.e., $x=K(3y+5)$

If $y=\frac{3}{5}$ when $x=10$

$⟹10=K(3\times \frac{3}{5}+5)$

$⟹10=K(\frac{9}{5}+5)$

$⟹10=K\times \frac{34}{5}$

$⟹K=10\times \frac{5}{34}=\frac{25}{17}$

$\therefore x=\frac{25}{17}(3y+5)$

When $x=35$ then,

$35=\frac{25}{17}(3y+5)$

$⟹35\times \frac{17}{25}=3y+5$

$⟹\frac{119}{5}=3y+5$

$⟹\frac{119}{5}-5=3y$

$⟹\frac{94}{5}=3y$

$\therefore y=\frac{94}{15}$