Question

Theresa is making smoothies. She made a table showing her favorite mixtures of blueberries and bananas in her smoothies.

Number of Blueberries 12 24
Number of Bananas 1 2
Which proportion represents the relationship shown?

Answer 1

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 \( \frac{12}{1} = \frac{24}{2} \).