To determine the constant of proportionality (or unit price) for a bag of popcorn at each theatre, you'll need to provide the prices and the quantities of popcorn for each theatre. Once I have that information, I can help you calculate the unit prices for each.
If you have the prices for each theatre, you can calculate the unit price using the formula:
\[ \text{Unit Price} = \frac{\text{Total Price}}{\text{Number of Bags}} \]
Please provide the necessary details for the calculations.