# How to avoid ambiguous wording: “Each has the same number of each type of flower”

I'm editing a math word problem that has the following ambiguous set up.

A florist has 18 carnations, 24 daisies, and 12 lilies. She wants to make flower arrangements that each have the same number of each type of flower.

The question is about greatest common factors, so the intended interpretation is that each arrangement has c carnations, d daisies, and l lilies. However, the second sentence can also be interpreted as meaning each arrangement has n carnations, n daisies, and n lilies.

How can I reword the second sentence to ensure the first interpretation without resorting to technical descriptions like above? (Added difficulty: the question is for 6th graders.)

Edit:
I should add that test items are best when they are clear and concise. I'm looking for a solution that is both.

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Re "clear": because all the numbers are divisible by 2, 3 and 6 there are three possible answers at present. See Daniel Harbour's answer – Andrew Leach Aug 16 '12 at 22:23
@AndrewLeach What I have posted is not the entire question (note there is no question in what I have posted). Please just focus on the specific sentence I have shared. – Excellll Aug 17 '12 at 2:00

Rather than ending the sentence with “that each have the same number of each type of flower”, end it with “that each have the same number of lilies, the same number of daisies, and the same number of carnations”.

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Thanks. This is the best option so far, but I'm going to wait a while in case someone comes up with something more concise. – Excellll Aug 16 '12 at 21:28

All the flowers of each type to be distributed evenly [or equally] between the bunches.

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The arrangements are intended to be all exactly the same. Identical describes that in English, and (if I remember my schooldays correctly) in mathematics.

Pick and choose bracketed portions as appropriate.

A florist has 18 carnations, 24 daisies, and 12 lilies. She wants to [use all the flowers and] make [the greatest number of] identical flower arrangements [that she can].

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I would suggest:

A florist has 18 carnations, 24 daisies, and 12 lilies. She wants to make flower arrangements that each have the same combination of the three types of flowers.

Or, as per @Gaffi's suggestion in the comments:

A florist has 18 carnations, 24 daisies, and 12 lilies. She wants to make flower arrangements that each have the same combination of all three types of flowers.

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Might it be better to change this to "...have the same combination of all three types of flowers." I could make the same arrangements using only one type of flower and discard the rest, otherwise. – Gaffi Aug 16 '12 at 21:19
@gaffi Added alternative :) – coleopterist Aug 17 '12 at 3:25

A florist has 18 carnations, 24 daisies, and 12 lilies. She wants to make identical flower arrangements such that each arrangement has the same proportion of flower types.

She would like to split the flowers evenly into identical flower arrangements.

As others have mentioned, you will want to specify greatest number of arrangements / smallest arrangement size.

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It's wordy, but the ambiguity should be gone.

A florist has 18 carnations, 24 daisies, and 12 lilies. She wants to make flower arrangements in such a way that each arrangement has the same number of carnations, daisies, and lilies as every other arrangement.

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All bunches of flowers must look the same.

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A florist has 18 carnations, 24 daisies, and 12 lilies. She [wants to sell all her flowers, and she] knows that everyone will want exactly the same bunch as everyone else: no one will want more carnations or fewer lilies or daisies than the next person. What’s the greatest number of bunches can she make?

I’ve added the bit about wanting to sell all her flowers, because otherwise a correct answer would be 12 (if each bunch has one of each flower and she fails to sell 6 carnations and 12 daisies).

Use of “greatest” (thanks to Andrew Leach for pointing out the need for revision here) clues students studying greatest common divisors in to what the question is after.

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Thanks. The final sentence of the question (not shown) specifies that she has no flowers left over, so that much is taken care of. I mostly wanted a way to get around this specific wording issue. – Excellll Aug 16 '12 at 21:25
I like the wording, but there is still more than one correct answer: 3 bunches of 6/8/4 or 6 bunches of 3/4/2. That's probably a deficiency in the original premise, but should there be an extra sentence "She needs to make the largest bunches she can" or "She needs to make as many bunches as she can"? Or, indeed, is the right answer that there are two answers? – Andrew Leach Aug 16 '12 at 21:30
@AndrewLeach. You’re right! There’s an implication, but no explicit statement, that the highest number of bunches is sought. I’ll fix it. – Daniel Harbour Aug 16 '12 at 21:41

A florist has 18 carnations, 24 daisies, and 12 lilies. She wants to make flower arrangements where there are the there are a certain number of carnations, daisies, and lilies in each arrangement. The number of each kind of flowers is the same in every arrangement, but not necessarily the same as the number of the other types.

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Does this work better for you?

A florist has 18 carnations, 24 daisies, and 12 lilies. She wants to make arrangements using all her flowers where the number of carnations is the same in each, as are the number of daisies, and lilies.

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The ambiguity is still there. Thanks though. :-/ – Excellll Aug 16 '12 at 21:10
@Excellll Edited mine. – Gaffi Aug 16 '12 at 21:30