Question

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. the cost of a bucket of popcorn is $8. 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?
○ $y = 12x + 8$
○ $y = 12x - 8$
○ $y = 14x + 8$
○ $y = 14x - 8$

Explanation:

Step1: Find cost per movie ticket

Let \( p \) be popcorn cost (\$8), \( t \) be ticket cost.
From first scenario: \( 8 + 4t = 56 \).
Subtract 8: \( 4t = 48 \).
Divide by 4: \( t = 12 \).

Step2: Form total cost equation

Total cost \( y \) = (ticket cost \( \times \) number of tickets) + popcorn cost.
So \( y = 12x + 8 \).

Answer:

\( y = 12x + 8 \) (the first option)