Final answer:
Hazel can make 24 arrangements with 1 rose and 1 mum in each vase.
Step-by-step explanation:
Hazel has 24 roses and 24 mums and wants to arrange them in vases with the same number of roses and mums.
To determine the greatest number of arrangements Hazel can make with the flowers she has, we need to find the greatest common factor (GCD) of 24 roses and 24 mums. The GCD represents the largest number of flowers that can be placed in each vase while ensuring that no flowers are left over.
The GCD of 24 and 24 can be calculated as follows:
GCD(24, 24) = 24
Since the GCD is 24, Hazel can create a maximum of 24 arrangements, with each vase containing 24 roses and 24 mums.
In this case, she can make 24 arrangements because she has 24 roses and 24 mums. Each arrangement will have 1 rose and 1 mum.