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Let's assume that the amount of water used for washing laundry is x.
According to the given ratio, the amount of water used for bathing is 9x and the amount of water used for washing the car is x/7.
Given that the amount of water used for bathing is 144L:
9x = 144
x = 144/9
x = <<16=16>>16L
Therefore, the Chen Family used 16L of water for washing laundry.