The ratio of roses to lilies in a garden is 3 to 2. If lilies and roses are the only flowers in the garden, what percentageof the garden's flowers are roses?
Accepted Solution
A:
Answer:Percentage of the garden's flowers that are roses = 60Step-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