To solve this problem, we need to determine the total number of riders that can fit on the roller coaster when 12 cars are linked together, given that two cars can hold a combined total of 14 riders.
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Find the number of riders per car: Since two cars hold 14 riders, we can find the capacity of one car by dividing the total number of riders by the number of cars:
\[ \text{Riders per car} = \frac{14 \text{ riders}}{2 \text{ cars}} = 7 \text{ riders per car} \]
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Calculate the total number of riders for 12 cars: Now that we know one car can hold 7 riders, we multiply the number of riders per car by the total number of cars (12 in this case):
\[ \text{Total riders for 12 cars} = 7 \text{ riders per car} \times 12 \text{ cars} = 84 \text{ riders} \]
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Conclusion: Therefore, when 12 cars are linked together, they can fit a total of 84 riders on the roller coaster at one time.
Thus, the final answer is:
84 riders.