If you use a serial protocol like Frame Relay which supports carrying multiple logical links on a physical link then connecting 38 client offices through your 3845 would be quite possible (if the serial link has sufficient capacity to aggregate the traffic from 38 client offices).
Or if you got a pair (1 would not be enough) of channelized serial links (like T3 or E3) and assigned a channel (or group of channels) to each client office it should be possible to connect 38 client offices through your 3845.
[edit] I just did some checking and according to this link:
http://www.cisco.com/en/US/prod/collateral/routers/ps5855/prod_qas0900aecd8016a953.html
table 5 indicates that channelized T3/E3 is supported on 7200 routers but not on 3800 routers. So there are not as many possibilities as I had thought for the 3800.
HTH
Rick
HTH
Rick