Which equation models the scoring in the final round and the outcome of the contest?
A. 4x – 12 + 132 = 12x + 56
B. 12x + 4x – 132 = 12x + 56
C. 12x – 4x + 132 = 12x + 56
D. 12x – 4x – 132 = 12x + 56
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To determine which equation models the scoring in the final round and the contest outcome, we should rearrange each option to see if they represent a valid scoring situation based on comparable terms.
Let’s look at each equation:
A. 4x – 12 + 132 = 12x + 56
Rearranging gives us (4x + 120 = 12x + 56).
This simplifies to (120 – 56 = 12x – 4x), which is valid.
B. 12x + 4x – 132 = 12x + 56
Simplifying gives us (16x – 132 = 12x + 56).
Rearranging leads to (4x = 188) which is also valid.
C. 12x – 4x + 132 = 12x + 56
This simplifies to (8x + 132 = 12x + 56).
Rearranging gives (76 = 4x), which is valid.
D. 12x – 4x – 132 = 12x + 56
This simplifies to (8x – 132 = 12x + 56).
Rearranging gives (-132 – 56 = 4x), leading to a different validity.
Depending on the context of the problem, each equation