To determine which scenario models the equation \(2x = 125 - 12x\), let's analyze both scenarios.
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Scenario 1: The Garcia family is driving towards a destination that is 125 miles away. After two hours of driving, they are half an hour short of reaching it. This means they have already driven for 2 hours and still need additional time to cover the remaining distance. The equation could represent a relationship involving the speed (rate) and time needed to reach the destination.
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Scenario 2: A construction company has three barrels of cement where the two full barrels weigh 125 pounds more than the third, which is half full. The equation could represent a relationship between the weights of the barrels.
To see which scenario fits the equation:
The equation \(2x = 125 - 12x\) can be rearranged to find \(x\):
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Combine like terms: \[ 2x + 12x = 125 \] \[ 14x = 125 \] \[ x = \frac{125}{14} \]
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The resulting value of \(x\) can represent a speed or a weight.
Given the context of the scenarios:
- For scenario 1, \(x\) could be the speed in miles per hour. Given that after driving for 2 hours, they are still short of reaching their vacation spot, this scenario seems to make sense with the equation.
- For scenario 2, \(x\) could represent a weight, but the relationship between the barrels and the weight is not an immediate match with the linear equation.
Considering the analysis, Scenario 1 is a better fit for the equation \(2x = 125 - 12x\).
Answer: 1
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