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

Answer:

$52$ roses and $117$ sunflowers

Step-by-step 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)

$\frac{5x}{5}=\frac{65}{5}$ (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!