the total cost for a bucket of popcorn and 4 movie tickets is $56. the total cost for the same size bucket…

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?\no y = 12x + 8\no y = 12x - 8\no y = 14x + 8\no y = 14x - 8

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?\no y = 12x + 8\no y = 12x - 8\no y = 14x + 8\no y = 14x - 8

Answer

Answer:

A. $y = 12x+8$

Explanation:

Step1: Find cost of one movie - ticket

Let the cost of one movie - ticket be $m$. We know that a bucket of popcorn ($p = 8$) and 4 movie - tickets cost $56$, so $p + 4m=56$. Substituting $p = 8$ into the equation: $8 + 4m=56$. Subtract 8 from both sides: $4m=56 - 8=48$. Divide both sides by 4: $m=\frac{48}{4}=12$.

Step2: Form the linear equation

The total cost $y$ of the popcorn and movie - tickets is the sum of the cost of the popcorn ($8$) and the cost of $x$ movie - tickets. The cost of $x$ movie - tickets is $12x$ (since each ticket costs $12$) and the cost of popcorn is $8$. So the equation is $y=12x + 8$.