To scoop or cut out a hole or groove, often violently or with a chisel, or to overcharge someone unfairly.
From Old French 'gouge,' from Latin 'gubia,' possibly from a Celtic source. Originally referred to a woodworking tool, then the action of using it, then metaphorically to overcharging.
When you 'gouge' someone for prices, you're using the metaphorical meaning from the 1800s—the word pictures someone being carved away, leaving them feeling hollowed out and robbed.
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