A gardener grows roses, tulips, and sunflowers in an 18-acre public garden. This year, she wants to plant twice as many acres of sunflowers as acres of tulips. She also wants wants to plant 6 more acres of roses than of sunflowers. How many acres of each flower should the gardener plant?

I need the system of equations for the question. Please help!

To solve this problem, let's start by assigning variables to each type of flower:

Let's say the number of acres of tulips is T.
The number of acres of sunflowers is S.
The number of acres of roses is R.

According to the given information, we can set up the following equations:

1) The total area of all the flowers is 18 acres:
T + S + R = 18

2) The gardener wants to plant twice as many acres of sunflowers as acres of tulips:
S = 2T

3) The gardener wants 6 more acres of roses than of sunflowers:
R = S + 6

Now we have our system of equations:

T + S + R = 18 ...(1)
S = 2T ...(2)
R = S + 6 ...(3)

By substituting equation (2) into equations (1) and (3), we can solve for the values of T, S, and R.