Final answer:
The equation that represents the relationship between the total cost of the popcorn and movie tickets and the number of movie tickets purchased is 3y + 6x = 80.
Step-by-step explanation:
The relationship between the total cost of the popcorn and movie tickets, represented by y, and the number of movie tickets purchased, represented by x, can be expressed using an equation.
Let's use the given information to form the equation.
From the first statement, the total cost for a bucket of popcorn and 4 movie tickets is $56. This can be written as:
3y + 4x = 56
From the second statement, the total cost for the same size bucket of popcorn and 6 movie tickets is $80. This can be written as:
3y + 6x = 80
So, the equation that represents the relationship between y and x is:
3y + 6x = 80