Flannery used $30$ lilies and $78$ roses to create six identical flower arrangements. $\newline$ Write an equation to describe the relationship between $l$ , the number of lilies, and $r$ , the number of roses. Do NOT use a mixed number.

Full solution

Q. Flannery used

30

lilies and

78

roses to create six identical flower arrangements.

\newline

Write an equation to describe the relationship between

l

, the number of lilies, and

r

, the number of roses. Do NOT use a mixed number.

Calculate Total Flowers: Determine the total number of lilies and roses used in the flower arrangements. $\newline$ Flannery used $30$ lilies and $78$ roses in total to create six identical flower arrangements.
Calculate Flowers per Arrangement: Calculate the number of lilies and roses in one flower arrangement. $\newline$ Since there are $6$ identical flower arrangements, we divide the total number of lilies and roses by $6$ to find the number in one arrangement. $\newline$ Number of lilies in one arrangement = Total lilies / Number of arrangements = $30 / 6 = 5$ $\newline$ Number of roses in one arrangement = Total roses / Number of arrangements = $78 / 6 = 13$
Write Equation for Ratio: Write the equation that relates the number of lilies and roses in one flower arrangement. $\newline$ Let $l$ represent the number of lilies and $r$ represent the number of roses in one flower arrangement. Since the arrangements are identical, the ratio of lilies to roses should be the same for each arrangement. $\newline$ The ratio of lilies to roses is $5$ lilies for every $13$ roses. $\newline$ Therefore, the equation is $\frac{l}{r} = \frac{5}{13}.$