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Question

# Given that $6 x=27 y$, find the ratio $y: x$ in simplest form.

Solution

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From the given cross products are the following holds

\begin{align*} \frac{6x}{27x}&=\frac{27y}{27x}&&\text{Divide each side by } 27x.\\ \textcolor{#4257b2}{\frac{y}{x}}&=\textcolor{#4257b2}{\frac{6}{27}}&&\text{Simplify}.\\ y:x&=6:27\\ \end{align*}

The ratio of the ratio $y : x \:$ is $\: 6 : 27$, or $2 : 9$. In simplest form, this ratio is $\textcolor{#4257b2}{2 : 9}$.

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