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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? ( i'm getting mixed up on this one, i'm usually good at word problems)

Answer :

Meliodas
Adding 2 movie tickets makes the cost go from 56 to 80. Since the difference is 24, each ticket cost $12. To find the bucket, use the original statement of 4 tickets ($48) plus 1 bucket of popcorn equals $56. The answer for each popcorn bucket is $8.

Answer with Step-by-step explanation:

Let b represent the cost of popcorn bucket and m represents the cost of 1 movie ticket.

The total cost for a bucket of popcorn and 4 movie tickets is $56.

⇒ b+4m= 56

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

⇒ b+6m=80

b+6m-(b+4m)=80-56

⇒ 2m=24

⇒ m=12

Putting value of m in b+4m=56

⇒ b+12×4=56

⇒b+48=56

⇒ b=56-48

⇒ b=8

Hence, cost of 1 movie ticket=$ 12

and cost of 1 bucket popcorn=$ 8

Let y be the total cost of the popcorn and movie tickets and x be the number of movie tickets that are purchased

⇒ 8+12x=y

Hence,  equation represents the relationship between y and x is:

y= 8+12x

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