A department store sells a pair of shoes with an 87% markup.

If the store sells the shoes for $193.21 then what is their non-markup price?

Let's assume the non-markup price of the shoes is x.

The markup price is 87% of x, which is 0.87x.
The actual selling price is the non-markup price plus the markup price, which is x + 0.87x = 1.87x.
We know that the actual selling price is $193.21, so 1.87x = $193.21.
Dividing both sides of the equation by 1.87, we get x = $193.21 / 1.87 = $103.45.
Therefore, the non-markup price of the shoes is $103.45. Answer: \boxed{103.45}.