Question

If rose needs to add 2 scoops of raspberries to every 5 cups of lemonade. At what ratio does the constant of proportionality appear

Answer 1

To find the constant of proportionality for the relationship between the scoops of raspberries and the cups of lemonade, we can express it as a ratio.

In this case, Rose adds 2 scoops of raspberries for every 5 cups of lemonade. The ratio of raspberries to lemonade can be expressed as:

\[
\text{Ratio} = \frac{\text{Scoops of Raspberries}}{\text{Cups of Lemonade}} = \frac{2}{5}
\]

Therefore, the constant of proportionality in this scenario is \(\frac{2}{5}\). This means that for every cup of lemonade, there are \(\frac{2}{5}\) of a scoop of raspberries added.

Answer 2

Table
Raspberries Lemonade
1 2.5
2 5
4 10
6 15

Answer 3

The provided table shows the relationship between the number of scoops of raspberries and the corresponding cups of lemonade. Let's analyze the data:

\[
\begin{array}{|c|c|}
\hline
\text{Raspberries (scoops)} & \text{Lemonade (cups)} \\
\hline
1 & 2.5 \\
2 & 5 \\
4 & 10 \\
6 & 15 \\
\hline
\end{array}
\]

To find the constant of proportionality, we can determine the ratio of raspberries to lemonade for each pair:

1. For 1 scoop of raspberries and 2.5 cups of lemonade:
\[
\text{Ratio} = \frac{1}{2.5} = \frac{1}{\frac{5}{2}} = \frac{1 \cdot 2}{5} = \frac{2}{5}
\]

2. For 2 scoops of raspberries and 5 cups of lemonade:
\[
\text{Ratio} = \frac{2}{5}
\]

3. For 4 scoops of raspberries and 10 cups of lemonade:
\[
\text{Ratio} = \frac{4}{10} = \frac{2}{5}
\]

4. For 6 scoops of raspberries and 15 cups of lemonade:
\[
\text{Ratio} = \frac{6}{15} = \frac{2}{5}
\]

In each case, the ratio of raspberries to lemonade is consistently \(\frac{2}{5}\). This confirms that the constant of proportionality in this relationship is \(\frac{2}{5}\).

This means for every 5 cups of lemonade, Rose consistently adds 2 scoops of raspberries, reflecting a proportional relationship.