To represent the relationship between the number of blueberries and bananas in Theresa's smoothies, we first look at the ratios provided in her table.
For the first mixture:
- Number of Blueberries: 12
- Number of Bananas: 1
The ratio of blueberries to bananas for this mixture is: \[ \frac{12}{1} = 12 \]
For the second mixture:
- Number of Blueberries: 24
- Number of Bananas: 2
The ratio of blueberries to bananas for this mixture is: \[ \frac{24}{2} = 12 \]
Both mixtures simplify to the same ratio of 12:1. Therefore, the proportion that represents the relationship shown would be:
\[ \frac{12 \text{ blueberries}}{1 \text{ banana}} = \frac{24 \text{ blueberries}}{2 \text{ bananas}} \]
This can also be expressed simply as: \[ \frac{12}{1} = \frac{24}{2} \]
Thus, the proportion that represents the relationship is \( \frac{12}{1} = \frac{24}{2} \).
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