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Which scenario models the equation 2x=125−12x ? Answer 1 or 2. After two hours of driving at the same rate of miles per hour, the Garcia family is one-half hour short of reaching their vacation spot, which is 125 miles away. A construction company has three barrels of cement. The two full barrels together weigh 125 pounds more than the third one, which is half full. (1 point)

1 answer

To determine which scenario models the equation \( 2x = 125 - 12x \), let's analyze both scenarios:

  1. Garcia Family Driving Scenario:

    • This scenario states that after two hours of driving, they are half an hour short of reaching a destination that is 125 miles away. If we assume \( x \) represents the miles per hour (rate), after 2 hours, they will have driven \( 2x \) miles. The total time needed to reach the vacation spot is \( \frac{125}{x} \) hours. Since they are half an hour short, we can express this as: \[ 2 + 0.5 = \frac{125}{x} \] Therefore, \( 2.5 = \frac{125}{x} \) which can be rearranged to \( 125 = 2.5x \). This does not match the equation \( 2x = 125 - 12x \).

  2. Construction Company Cement Barrel Scenario:

    • In this scenario, there are three barrels of cement. Let \( x \) be the weight of the third barrel when it is half full. The two full barrels together weigh 125 pounds more than the third barrel. This can be expressed as: \[ 2x + 125 = 3x \] Rearranging gives \( 2x = 125 - x \), which is not exactly the same form as \( 2x = 125 - 12x \) but can lead to similar reasoning.

Therefore, while the first scenario does not match, we find that the second scenario involving the construction company might lead to a similar form when analyzing weights, but there seems to be a discrepancy with the coefficient for the third term in the provided equation.

However, if the focus is on which scenario could potentially relate better to the algebraic structure, then the construction company scenario seems more applicable. But neither matches perfectly with the original equation \( 2x = 125 - 12x \).

In conclusion, if forced to choose, Answer 2 appears to be the more suitable scenario, although neither scenario directly models the given equation accurately without an additional piece of information or assumption.