To find out how much Molly's family plans to spend on meals, we can break it down into steps.
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Calculate the amount set aside for gasoline and motel rooms: The family plans to spend \( \frac{3}{5} \) of the $3000 on gasoline and motel rooms. \[ \text{Amount for gasoline and motel} = \frac{3}{5} \times 3000 \] \[ = 1800 \]
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Calculate the remainder after spending on gasoline and motel rooms: \[ \text{Remainder} = 3000 - 1800 \] \[ = 1200 \]
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Calculate the amount for meals: The family plans to spend \( \frac{1}{2} \) of the remainder on meals. \[ \text{Amount for meals} = \frac{1}{2} \times 1200 \] \[ = 600 \]
Therefore, Molly's family plans to spend \( \boxed{600} \) dollars on meals.