Suppose that 23 inches of wire costs 92 cents.
At the same rate, how much (in cents) will 17 inches of wire cost?
To find the cost of 17 inches of wire, we can use a proportion. Since 23 inches of wire costs 92 cents, we can set up the proportion:
$\dfrac{23 \text{ inches}}{92 \text{ cents}} = \dfrac{17 \text{ inches}}{x \text{ cents}}$ where $x$ is the unknown number of cents that 17 inches will cost.
Cross-multiplying gives us $23x = 17(92)$ or $23x = 1564$.
Dividing both sides by 23 gives us $x = \boxed{68}$ cents. Answer: \boxed{68}.