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?
$y = 14x + 8$
$y = 14x - 8$
$y = 12x - 8$
$y = 12x + 8$

Explanation:

Step1: Find cost per movie ticket

Let \( p \) be popcorn cost (\( \$8 \)), \( t \) be ticket cost. From two scenarios:

1. \( 8 + 4t = 56 \)
2. \( 8 + 6t = 80 \)

Subtract first from second: \( (8 + 6t) - (8 + 4t) = 80 - 56 \)
Simplify: \( 2t = 24 \) → \( t = \$12 \).

Step2: Form total cost equation

Total cost \( y \) = popcorn cost + (ticket cost × number of tickets \( x \)).
Popcorn is \( \$8 \), ticket cost \( \$12 \). So \( y = 12x + 8 \).

Answer:

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