Question

There are 90 yellow flowers, 54 red flowers, and 36 white flowers for centerpieces. If the flowers need to be divided equally into separate centerpieces with the same number of each color of flower in each centerpiece, how many different centerpieces will there be?

Answer 1

You can create the fewest centerpieces for the smallest number of any color, which is 2 centerpieces using the white flowers. Therefore, you will have 2 centerpieces with an equal number of each color of flower in each centerpiece.

Explanation:

First, find the GCD of 90, 54, and 36:

Find the GCD of 90 and 54:

GCD(90, 54) = 18

Find the GCD of the result (18) and 36:

GCD(18, 36) = 18

So, the GCD of 90, 54, and 36 is 18.

Now, you can create centerpieces with 18 flowers of each color (yellow, red, and white) in each centerpiece. To find out how many centerpieces you can create, divide the total number of each color by 18:

Number of yellow flowers / 18 = 90 / 18 = 5 centerpieces

Number of red flowers / 18 = 54 / 18 = 3 centerpieces

Number of white flowers / 18 = 36 / 18 = 2 centerpieces

You can create the fewest centerpieces for the smallest number of any color, which is 2 centerpieces using the white flowers. Therefore, you will have 2 centerpieces with an equal number of each color of flower in each centerpiece.