12. If $$ \frac{2 x-y}{x+3 y}=\frac{2}{3} $$, what is the ratio of $$ x $$ to (A) $$ \frac{2}{3} $$ (B) $$ \frac{3}{2} $$ (C) $$ \frac{9}{4} $$ (D) $$ \frac{4}{9} $$ (E) $$ \frac{3}{4} $$

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The ratio of $$ x $$ to $$ y $$ is $$ \frac{9}{4} $$, so the correct answer is (C). To solve for the ratio of $$ x $$ to $$ y $$, we can start by setting up the given equation: $$ \frac{2x - y}{x + 3y} = \frac{2}{3} $$ To find the ratio $$ \frac{x}{y} $$, we need to isolate $$ x $$ in terms of $$ y $$. Let's cross-multiply to get rid of the fractions: $$ 3(2x - y) = 2(x + 3y) $$ Now, distribute the numbers on both sides: $$ 6x - 3y = 2x + 6y $$ Next, we want to get all the $$ x $$ terms on one side and all the $$ y $$ terms on the other side. Let's move the $$ x $$ terms to the left and the $$ y $$ terms to the right: $$ 6x - 2x = 6y + 3y $$ This simplifies to: $$ 4x = 9y $$ Now, to find the ratio $$ \frac{x}{y} $$, we divide both sides by $$ y $$: $$ \frac{4x}{y} = 9 $$ And then divide both sides by 4: $$ \frac{x}{y} = \frac{9}{4} $$ So the ratio of $$ x $$ to $$ y $$ is $$ \frac{9}{4} $$, which corresponds to option (C).

12. If \( \frac{2 x-y}{x+3 y}=\frac{2}{3} \), what is the ratio of \( x \) to (A) \( \frac{2}{3} \) (B) \( \frac{3}{2} \) (C) \( \frac{9}{4} \) (D) \( \frac{4}{9} \) (E) \( \frac{3}{4} \)

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12. If \( \frac{2 x-y}{x+3 y}=\frac{2}{3} \), what is the ratio of \( x \) to (A) \( \frac{2}{3} \) (B) \( \frac{3}{2} \) (C) \( \frac{9}{4} \) (D) \( \frac{4}{9} \) (E) \( \frac{3}{4} \)

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