To determine the constant of proportionality (unit price) for the bag of popcorn at each theatre, we need the total cost and quantity for each theatre. Since the information for the prices isn't provided, I'm using hypothetical prices to illustrate how to calculate unit prices. Please fill in the correct amounts you have.
Example Calculation for Unit Prices:
Let's say the costs and quantities of popcorn bags at various theatres are as follows:
- Big Screen: $5.00 for 2 bags
- Fantastic Flicks: $7.50 for 3 bags
- Movie Mania: $4.25 for 1 bag
- Perfect Picture: $8.00 for 4 bags
Now we can calculate the unit price for each theatre:
- Big Screen: \( \frac{5.00}{2} = 2.50 \) (Unit Price = $2.50 per bag)
- Fantastic Flicks: \( \frac{7.50}{3} = 2.50 \) (Unit Price = $2.50 per bag)
- Movie Mania: \( \frac{4.25}{1} = 4.25 \) (Unit Price = $4.25 per bag)
- Perfect Picture: \( \frac{8.00}{4} = 2.00 \) (Unit Price = $2.00 per bag)
So, you would fill out:
- Big Screen: $2.50 per bag of popcorn
- Fantastic Flicks: $2.50 per bag of popcorn
- Movie Mania: $4.25 per bag of popcorn
- Perfect Picture: $2.00 per bag of popcorn
For Question 2:
The theatre with the best deal for popcorn is Perfect Picture at $2.00, and the theatre with the worst deal for popcorn is Movie Mania at $4.25.
For Question 3:
Let’s calculate how much you'd save by choosing Perfect Picture over Fantastic Flicks for 3 bags.
- Cost from Perfect Picture for 3 bags: \( 3 \times 2.00 = 6.00 \)
- Cost from Fantastic Flicks for 3 bags: \( 3 \times 2.50 = 7.50 \)
Now, find the difference:
Savings = \( 7.50 - 6.00 = 1.50 \)
So you would fill out:
Saving = $1.50
Please replace the example prices with the actual prices to complete your assignment correctly.