Question

Do you want to make bouquets of balloons. You choose 18 yellow, 30 blue, and 42 red balloons. Each bouquet will have the same number of each color. What is the greatest possible number of bouquets you can make?

Answer 1

The greatest number of bouquets made from 18 yellow, 30 blue, and 42 red balloons is 6, where each bouquet contains 3 yellow, 5 blue, and 7 red balloons, found by calculating the greatest common divisor.

Step-by-step explanation:

The question is asking for the greatest possible number of bouquets that can be made using the balloons provided in equal proportions. To solve this, we need to find the greatest common divisor (GCD) of the quantities of the different colored balloons, which are 18 yellow, 30 blue, and 42 red balloons.

We start by listing the factors of each number:

• Factors of 18: 1, 2, 3, 6, 9, 18
• Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
• Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42

The greatest common factor that appears in all three lists is 6. Therefore, we can make the greatest number of bouquets by dividing each balloon color by 6:

• 18 yellow balloons ÷ 6 = 3 yellow balloons per bouquet
• 30 blue balloons ÷ 6 = 5 blue balloons per bouquet
• 42 red balloons ÷ 6 = 7 red balloons per bouquet

So, the greatest possible number of bouquets is 6, with each bouquet containing 3 yellow, 5 blue, and 7 red balloons.