The problem describes a garden with 54 flowers consisting of roses, sunflowers, and marigolds. We are given the number of roses (21) and sunflowers (18), and we need to find the number of marigolds. Then, we need to find the ratio of roses to sunflowers to marigolds in its simplest form.

1. Problem Description

The problem describes a garden with 54 flowers consisting of roses, sunflowers, and marigolds. We are given the number of roses (21) and sunflowers (18), and we need to find the number of marigolds. Then, we need to find the ratio of roses to sunflowers to marigolds in its simplest form.

2. Solution Steps

First, we need to find the number of marigolds. The total number of flowers is

5

4. The number of roses is 21 and the number of sunflowers is

1

8. Therefore, the number of marigolds is:

$54 - 21 - 18 = 15$

Now we have the number of roses, sunflowers, and marigolds:

Roses: 21

Sunflowers: 18

Marigolds: 15

The ratio of roses to sunflowers to marigolds is $21:18:15$.

We need to simplify this ratio. We find the greatest common divisor (GCD) of 21, 18, and

1

5. The factors of 21 are 1, 3, 7,

2

1. The factors of 18 are 1, 2, 3, 6, 9,

1

8. The factors of 15 are 1, 3, 5,

1

5. The GCD is

3.

We divide each number in the ratio by 3:

$21 / 3 = 7$

$18 / 3 = 6$

$15 / 3 = 5$

So, the simplified ratio is $7:6:5$.

3. Final Answer

$7:6:5$