To determine the constant of proportionality in the situation described, we first need to understand the ratio of raspberry scoops to lemonade cups.
According to the information provided, Rosie needs to add 2 scoops of raspberry for every 5 cups of lemonade. This can be expressed as the ratio of raspberry scoops to cups of lemonade:
\[ \text{Ratio} = \frac{\text{scoops of raspberry}}{\text{cups of lemonade}} = \frac{2}{5} \]
The constant of proportionality in this case is the value that relates the two quantities, which is obtained from the ratio. For every 1 cup of lemonade, the amount of raspberry scoops needed can be calculated as follows:
To find the amount of raspberry scoops per cup of lemonade:
\[ \text{Constant of proportionality} = \frac{2 \text{ scoops}}{5 \text{ cups}} = 0.4 \text{ scoops per cup} \]
Thus, the constant of proportionality that describes the relationship between scoops of raspberry and cups of lemonade is:
0.4 scoops of raspberry for every cup of lemonade.