To determine if the table is set up correctly based on the quantities of roses and daffodils in a bouquet, we first analyze the numbers provided:
You mentioned:
- Daffodils: 3, 6, 10, 12
- Roses: 4, 8, 12, 16
We also know that in each bouquet, there are 4 roses and 3 daffodils. This means that the ratio of roses to daffodils is 4:3.
Next, let's examine the ratios provided in the table:
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For Daffodils:
- 3 daffodils = 3
- 6 daffodils = 6
- 10 daffodils = 10
- 12 daffodils = 12
-
For Roses:
- 4 roses = 4
- 8 roses = 8
- 12 roses = 12
- 16 roses = 16
Now, let's look at the ratios of roses to daffodils for the pairs given in the table:
- For (3 daffodils, 4 roses): Ratio is \( \frac{4}{3} \)
- For (6 daffodils, 8 roses): Ratio is \( \frac{8}{6} = \frac{4}{3} \)
- For (10 daffodils, 12 roses): Ratio is \( \frac{12}{10} = \frac{6}{5} \)
- For (12 daffodils, 16 roses): Ratio is \( \frac{16}{12} = \frac{4}{3} \)
By examining the ratios, we can see that the ratios of roses to daffodils do not consistently represent the same proportion. While some of them equal \( \frac{4}{3} \), indicating incorrect set up for a uniform ratio across pairs, others differ (like \( \frac{6}{5} \)).
Based on this evaluation, the table is not set up correctly because all the ratios in the table cannot be simplified to \( \frac{3}{4} \), which is the correct ratio derived from the original bouquet of 3 daffodils and 4 roses.
Therefore, the correct response is: The table is not set up correctly because all the ratios in the table cannot be simplified to \( \frac{3}{4} \).