Kelly's art teacher asked him to draw a rectangle with a length of $6$ inches and a width of $10$ inches.  After Kelly does so, his teacher changes her mind and asks him to draw a proportional rectangle that has a length of $9$ inches.  How many inches wide is the new rectangle?
This means that the ratio of the length to the width is the same for both rectangles. So, I can set up a proportion equation: $\frac{6}{10} = \frac{9}{w}$, where $w$ is the unknown width. To solve for $w$, I can cross-multiply and get: $6w = 90$. Dividing both sides by $6$, I get: $w = 15$. So, the new rectangle has a width of $15$ inches. 