<human>:  Twenty dozen cups cost $1200 less than the total cost of half a dozen plates sold at $6000 each. Calculate the total cost of buying each cup.
<bot>: How many half a dozen plates are sold? ** Since a dozen has 12 items, half a dozen plates are 12/2 = <<6=6>>6
How much do half a dozen plates cost? ** Half a dozen plates sold at $6000 each cost 6*$6000 = $<<6*6000=36000>>36000
How much do twenty dozen cups cost? ** Twenty dozen cups cost $1200 less than the total cost of half a dozen plates, meaning the twenty dozen cups cost a total of $36000-$1200 = 34800
How many cups are in a dozen? ** Since a dozen has 12 items, twenty dozen cups are 20*12 = <<20*12=240>>240 cups.
How much does each cup cost? ** If the twenty dozen cups cost $34800, each cup costs $34800/240=$<<34800/240=145>>145
#### 145