1. The problem states that Flannery used 30 lilies and 78 roses to create six identical flower arrangements. 2. We need to write an equation relating $l$, the number of lilies per arrangement, and $r$, the number of roses per arrangement. 3. Since the total lilies are 30 and total roses are 78, and there are 6 identical arrangements, each arrangement has $\frac{30}{6}$ lilies and $\frac{78}{6}$ roses. 4. Calculate the number of lilies per arrangement: $$l = \frac{30}{6} = 5$$ 5. Calculate the number of roses per arrangement: $$r = \frac{78}{6} = 13$$ 6. The relationship between $l$ and $r$ is that each arrangement has 5 lilies and 13 roses. 7. Therefore, the equation describing the relationship is: $$l = 5 \quad \text{and} \quad r = 13$$ 8. Alternatively, if you want a single equation relating $l$ and $r$, since both are constants per arrangement, you can write: $$\frac{l}{5} = \frac{r}{13}$$ which shows the ratio of lilies to roses per arrangement. Final answer: $$\frac{l}{5} = \frac{r}{13}$$