[carsten]

You (or whoever assigned this problem to you) are using a backwards (and in my opinion non-standard) definition of markup. In any context I have encountered, markup is a percentage applied to purchase cost, and elitegimp's are based on that definition.

In your examples, the "markup" is the discount you'd have to apply to the selling price to get the purchase cost back. For example, a selling price of $1.25 represents a 25% markup over the purchase cost of $1, but you'd have to subtract 20% of $1.25 to get back to $1.

The formula to calculate that percentage is

ass_backwards_non_standard_markup = (1 - cost/price) * 100%.

Solving this equation for calculating cost and price given the respective other two quantities is left as an exercise for the reader.

Hope this helps,

-Carsten

P.S. Aren't we a bit off topic here? This has nothing to do with probability theory.