Jackie is making flower arrangements. She has 2 roses and 4 daisies. If Jackie wants to make all the arrangements identical and have no flowers left over, what is the greatest number of flower arrangements she can make? help<3

Let's explore possible case scenarios.

Case A) Each person gets a rose and a daisy (2 flowers per person)

In this case, Jackie can make 2 such arrangements because she has 2 roses. We have 2 left over daisies.

Case B) Each person gets a rose only (1 flower per person)

Only two arrangements are possible for the same reason as case A. In this situation, we have 4 left over daisies.

Case C) Each person gets a daisy only (1 flower per person)

We have 4 arrangements possible because we have 4 daisies. The left over flowers are the 2 roses.

Case D) Each person gets 2 roses

Only one such arrangement is possible, so this only applies to one person really. You can say that 2/2 = 1. We have 4 left over daisies in this case.

Case E) Each person gets 2 daisies

Since 4/2 = 2, this means we can make 2 arrangements. There are 2 left over roses.

Case F) Each person gets 2 daisies and 1 rose

We can see that 4/2 = 2 and 2/2 = 1, meaning that we can make at most 2 arrangements here. There are no leftovers. In contrast, the other cases do have leftovers of some kind.

In short, you can do trial and error to see which case works to fit the conditions your teacher set. Case F is what we go for to have each flower bouquet consist of 2 daisies and 1 rose. We'll get 2 bouquets possible. Notice how cases A through E have at least one left over flower (either of one kind or both types), while case F has no leftovers.