I came across an example problem that I don't fully understand. Here is the problem and solution:
A 1000 bond with semi-annual coupons at $i^{(2)}$ = 6% matures at par on October 15, 2020.The bond is purchased on June 28, 2005 to yield the investor $i^{(2)}$ = 7%. What is the purchase price? Assume simple interest between bond coupon dates, and the following day count: $$\begin{array} {|c|} \hline Date & Day of the Year \\ \hline April 15 & 105 & \\ \hline June 28 & 179 & \\ \hline October 15 & 288 & \\ \hline \end{array}$$
We start by finding the price of the bond on the previous coupon date: April 15, 2005. On that date, there are 31 coupons of $30 each left and the price is:
$30*\frac{1-\frac{1}{1.035}^{31}}{.035} +1000\frac{1}{1.035}^{31} \approx 906.32$
Therefore, the price on June 28 is (note the use of simple interest for interim accumulation)
$906.32*(1+\frac{179-105}{182.5}*.035)=906.32*(1+\frac{74}{182.5}*.035) \approx 919.18$
This is a form of the flat price, not market price, and the reason why we use the flat price is that the question asks for the purchase price.
What I don't understand in all of that is, where did the 182.5 came from?