Question

A florist was looking at her flower order. The ratio of roses to sunflowers was 4 to 9. When she was done, she realized there were 65 MORE sunflowers than roses. How many of each flower was there?

Answer 1

`52` roses and
`117` sunflowers

Explanation:

Since the ratio of roses to sunflowers is
`4:9`, we can represent how many there are of each as
`4x` and
`9x`, respectively. We know that there are
`65` more sunflowers than roses, so we can set up the following equation to solve for
`x`:

`4x+65=9x`

Solving for
`x`, we get:

`4x+65=9x`

`4x+65-4x=9x-4x` (Subtract
`4x` from both sides of the equation to isolate
`x`)

`65=5x` (Simplify)

`5x=65` (Symmetric Property of Equality)

`(5x)/(5)=(65)/(5)` (Divide both sides of the equation by
`5` to get rid of
`x`'s coefficient)

`x=13` (Simplify)

Therefore, since
`x=13`, we know that there are
`4x=4*13=52` roses and
`9x=9*13=117` sunflowers. Hope this helps!