Answer:
[tex]52[/tex] roses and [tex]117[/tex] sunflowers
Step-by-step explanation:
Since the ratio of roses to sunflowers is [tex]4:9[/tex], we can represent how many there are of each as [tex]4x[/tex] and [tex]9x[/tex], respectively. We know that there are [tex]65[/tex] more sunflowers than roses, so we can set up the following equation to solve for [tex]x[/tex]:
[tex]4x+65=9x[/tex]
Solving for [tex]x[/tex], we get:
[tex]4x+65=9x[/tex]
[tex]4x+65-4x=9x-4x[/tex] (Subtract [tex]4x[/tex] from both sides of the equation to isolate [tex]x[/tex])
[tex]65=5x[/tex] (Simplify)
[tex]5x=65[/tex] (Symmetric Property of Equality)
[tex]\frac{5x}{5}=\frac{65}{5}[/tex] (Divide both sides of the equation by [tex]5[/tex] to get rid of [tex]x[/tex]'s coefficient)
[tex]x=13[/tex] (Simplify)
Therefore, since [tex]x=13[/tex], we know that there are [tex]4x=4*13=52[/tex] roses and [tex]9x=9*13=117[/tex] sunflowers. Hope this helps!
