### Instruction: Solve for $r$: \[\frac{r-45}{2} = \frac{3-2r}{5}.\].### Response: Let's multiply both sides by 10.
That gives us $5(r-45)=2(3-2r)$.
Expanding gives $5r-225=6-4r$.
Adding $4r$ to both sides gives $9r-225=6$.
Adding $225$ to both sides gives $9r=231$.