The total cost for a bucket of popcorn and 4 movie tickets is $56. the total cost for the same size bucket of popcorn and 6 movie tickets is $80. which equation represents the relationship between y, the total cost of the popcorn and movie tickets, and x, the number of movie tickets that are purchased?

The required equation is, y = 8 + 12 x

Step-by-step explanation:

Let p be the price of one bucket of popcorn and t be the price of one ticket,

Since, the total cost for a bucket of popcorn and 4 movie tickets is $56

⇒ p + 4t = 56  (1)

And, the total cost for the same size bucket of popcorn and 6 movie tickets is $80.

⇒ p + 6t = 80 (2)

Equation (1) - Equation (2),

⇒ -2 t = - 24 ⇒ t = 12

By substituting this value in equation (1),

We get, p + 48 = 56 ⇒ p = 8

Thus, the price of one bucket of popcorn = $8

And, the price of one ticket = $12

Thus, the total price (y) of one bucket of popcorn and x tickets is,

y = 8 + 12 x

Which is the required equation.