ANSWER
[tex] \frac{x}{y} = \frac{4}{9} [/tex]
EXPLANATION
The given equation is
[tex] \frac{x}{5} = \frac{2}{3} = \frac{5}{y} [/tex]
We separate the above equation into two different equations.
[tex] \frac{x}{5} = \frac{2}{3} ...eqn1[/tex]
[tex]\frac{2}{3} = \frac{5}{y} ...eqn2[/tex]
From equation (1), we cross multiply to obtain,
[tex]3x = 10[/tex]
This implies that,
[tex]x = \frac{10}{3} [/tex]
From equation (2), we cross multiply to get,
[tex]2y = 15[/tex]
This implies that,
[tex]y = \frac{15}{2} [/tex]
We divide x by y to get,
[tex] \frac{x}{y} = \frac{ \frac{10}{3} }{ \frac{15}{2} } [/tex]
This is the same as,
[tex] \frac{x}{y} = \frac{10}{3} \div \frac{15}{2} [/tex]
[tex] \frac{x}{y} = \frac{10}{3} \times \frac{2}{15} [/tex]
[tex] \frac{x}{y} = \frac{2}{3} \times \frac{2}{3} [/tex]
[tex] \frac{x}{y} = \frac{4}{9} [/tex]
The correct answer is B
