Question

The colored roses in the bouquet of flowers are red, yellow, and pink. The ratio of the number of red to the number of yellow to the number of pink in the closet is 7:4:6, respectively. If there are more than 7 yellow colored roses, what is the minimum number of total roses in the bouquet?

• A. 8
• B. 12
• C. 14
• D. 24
• E. 34

Hint:

When working with ratios, always find the smallest possible multiple that satisfies the given condition.

Answer 1

The Correct Option is D

Step 1: Use the ratio.
We are given the ratio of red to yellow to pink roses as 7:4:6. Let the number of red, yellow, and pink roses be \( 7x \), \( 4x \), and \( 6x \), respectively. The total number of roses is: \[ 7x + 4x + 6x = 17x \] Step 2: Find the minimum number of yellow roses.
We are told that there are more than 7 yellow roses, so: \[ 4x>7 \] \[ x>\frac{7}{4} = 1.75 \] Thus, the smallest integer value for \( x \) is 2.
Step 3: Calculate the total number of roses.
Substitute \( x = 2 \) into the total number of roses: \[ 17x = 17 \times 2 = 34 \] Thus, the minimum number of roses is 34. Therefore, the correct answer is (D) 24.