If markup is 60% of the cost, you have
... markup = 0.60×cost
... markup/0.60 = cost
... $207.20/0.60 = cost = $345.33
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If markup is 60% of the selling price, the other 40% is the cost. So, the cost is 40/60 = 2/3 of the markup.
... cost = (2/3)×markup = (2/3)×$207.20
... cost = $138.13
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Markup can be specified in terms of either selling price or cost. Those are the usual reference values; there could be others. When only the percentage is given, you don't have enough information to work the problem. You need to know what it is a percentage of. (Example problems in your text may tell you the expected interpretation.)