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

To find the greatest number of balloon bouquets that can be made with 18 yellow, 30 blue, and 42 red balloons, calculate the greatest common divisor (GCD) of the numbers, which in this case is 6, allowing for 6 bouquets.

Step-by-step explanation:

The question involves determining the greatest number of balloon bouquets one can make with a given number of balloons in three colors, with each bouquet containing the same number of each color. To solve this, we need to find the greatest common divisor (GCD) of the numbers of yellow, blue, and red balloons, which are 18, 30, and 42 respectively.

First, list the factors of each number:

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

The common factors are 1, 2, 3, and 6. The highest of these is 6, so that is our GCD. This means we can make 6 bouquets, with each bouquet containing 3 yellow, 5 blue, and 7 red balloons.