Question

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 percentage

of the garden's flowers are roses?​

Answer 1

Percentage of the garden's flowers that are roses = 60

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

`\frac{\texttt{Number of roses}}{\texttt{Number of lillies}}=(3)/(2)\\\\\frac{r}{\texttt{Number of lillies}}=(3)/(2)\\\\\texttt{Number of lillies}=(2)/(3)r`

Now we need to find what percentage of the garden's flowers are roses.

`\texttt{Percentage of roses = }\frac{\texttt{Total number of roses}}{\texttt{Total number of flowers}}* 100\\\\\texttt{Total number of flowers}=\texttt{Total number of flowers}+\texttt{Total number of lillies}\\\\\texttt{Total number of flowers}=r+(2)/(3)r=(5)/(3)r\\\\\texttt{Percentage of roses = }(r)/((5)/(3)r)* 100=(3)/(5)* 100=60\%`

Percentage of the garden's flowers that are roses = 60