Answered

The total cost for a bucket of popcorn and 4 movie tickets is [tex]$\$[/tex] 56[tex]$. The total cost for the same size bucket of popcorn and 6 movie tickets is $[/tex]\[tex]$ 80$[/tex]. The cost of a bucket of popcorn is [tex]$\$[/tex] 8[tex]$.

Which equation represents the relationship between $[/tex]y[tex]$, the total cost of the popcorn and movie tickets, and $[/tex]x[tex]$, the number of movie tickets that are purchased?

A. $[/tex]y = 12x + 8[tex]$

B. $[/tex]y = 12x - 8[tex]$

C. $[/tex]y = 14x + 8[tex]$

D. $[/tex]y = 14x - 8$



Answer :

GinnyAnswer
To find the equation that represents the relationship between [tex]\( y \)[/tex] (the total cost of the popcorn and movie tickets) and [tex]\( x \)[/tex] (the number of movie tickets purchased), we need to break down the information given and follow a step-by-step approach:

1. Identify the known variables:
- Total cost for popcorn and 4 movie tickets is \[tex]$56. - Total cost for popcorn and 6 movie tickets is \$[/tex]80.
- The cost of a bucket of popcorn is \[tex]$8. 2. Set up the relationship in terms of movie tickets: Let's denote the cost of one movie ticket as \( C \). 3. Establish two equations based on the given information: - For 4 movie tickets and 1 bucket of popcorn: \[ 4C + 8 = 56 \] - For 6 movie tickets and 1 bucket of popcorn: \[ 6C + 8 = 80 \] 4. Solve the first equation for \( C \): \[ 4C + 8 = 56 \] Subtract 8 from both sides: \[ 4C = 48 \] Divide by 4: \[ C = 12 \] 5. Verify \( C \) with the second equation: \[ 6C + 8 = 80 \] Substitute \( C = 12 \) into the equation: \[ 6(12) + 8 = 80 \] \[ 72 + 8 = 80 \] The verification confirms \( C = 12 \) or \$[/tex]12 per movie ticket.

6. Formulate the equation [tex]\( y \)[/tex]:
- [tex]\( y \)[/tex] is the total cost of [tex]\( x \)[/tex] number of movie tickets and 1 bucket of popcorn.
[tex]\[ y = 12x + 8 \][/tex]

Thus, the equation representing the relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] is:

[tex]\[ y = 12x + 8 \][/tex]

Therefore, the correct option is [tex]\( y = 12x + 8 \)[/tex].