Answer:
Percentage of the garden's flowers that are roses = 60
Step-by-step explanation:
The ratio of roses to lilies in a garden is 3 to 2.
Let number of roses in the garden be r.
We have
[tex]\frac{\texttt{Number of roses}}{\texttt{Number of lillies}}=\frac{3}{2}\\\\\frac{r}{\texttt{Number of lillies}}=\frac{3}{2}\\\\\texttt{Number of lillies}=\frac{2}{3}r[/tex]
Now we need to find what percentage of the garden's flowers are roses.
[tex]\texttt{Percentage of roses = }\frac{\texttt{Total number of roses}}{\texttt{Total number of flowers}}\times 100\\\\\texttt{Total number of flowers}=\texttt{Total number of flowers}+\texttt{Total number of lillies}\\\\\texttt{Total number of flowers}=r+\frac{2}{3}r=\frac{5}{3}r\\\\\texttt{Percentage of roses = }\frac{r}{\frac{5}{3}r}\times 100=\frac{3}{5}\times 100=60\%[/tex]
Percentage of the garden's flowers that are roses = 60
