Question

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?
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Answer 1

Let's explore possible case scenarios.

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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.

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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.

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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.

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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.

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Case E) Each person gets 2 daisies

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

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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.

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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.