A cider recipe calls for 3 green apples for every 5 red apples. We can create a table to show some equivalent ratios.

We can see from the table that $r$ is always $\frac53$ as large as $g$ and that $g$ is always $\frac35$ as large as $r$.

• When we know the number of green apples and want to find the number of red apples, we can write:

  $\displaystyle r=\frac53g$

  In this equation, if $g$ changes, $r$ is affected by the change, so we refer to $g$ as the independent variable and $r$ as the dependent variable.

  We can use this equation with any value of $g$ to find $r$. If 270 green apples are used, then $\frac53 \boldcdot (270)$ or 450 red apples are used.

• When we know the number of red apples and want to find the number of green apples, we can write:

  $\displaystyle g=\frac35r$

  In this equation, if $r$ changes, $g$ is affected by the change, so we refer to $r$ as the independent variable and $g$ as the dependent variable.

  We can use this equation with any value of $r$ to find $g$. If 275 red apples are used, then $\frac35 \boldcdot (275)$ or 165 green apples are used.