Wow. First, questions of this type usually get a better reception at sci.electronics.basics.
Second, you've got a couple of resistors bass-ackwards on your first diagram. A non-inverting amplifier with a gain of 3 might look like this (view in fixed font or M$ Notepad):
| | Vcc | | V(in) |\| | o--------|+\ V(out) = 3*V(in) | | >------o---o | .---|-/ | | | |/| | | | | | | Vee | | | ___ | | V(in) o-----|___|---' | | 20K | .-. | | | | 10K | | | '-' | | | GND | created by Andy´s ASCII-Circuit v1.24.140803 Beta
Now, for your problem. You're not talking about an offset voltage (usually used to describe cancelling out the op amp V(os), but adding or summing two voltages in a non-inverting amplifier.
As is frequently the case, National Semiconductor AN-31 calls out with an answer. On page two, it describes a non-inverting summing amplifier which will do the job for you (assuming the output impedance of your V(in) is fairly low):
| ___ | .---|___|---. | | 100K | | | Vcc | | ___ | |\| | | .--|___|--o---|-\ | | | 20K | >----o----o | === .--|+/ | GND | |/| | | Vee | | | | | V(in) ___ | | o---|___|-o | 100K | | | | ___ | | o---|___|-' | 33.3mV 100K | | created by Andy´s ASCII-Circuit v1.24.140803 Beta
Here's the way it works: The op amp non-inverting input sees the average of V(in) and 33.3mV, or [V(in) + 33.3mV]/2. The two resistors at the inverting side are set up for a gain of 6. That results in a total gain of [V(in) * 3] + 100mV, which is what you were looking for to begin with.
With a 5V supply, you might get close enough for government work by using a 5.1K/33 ohm resistive voltage divider to get the 33mV. The important thing is to keep both impedances low.
Download this app-note and keep it with you. It's a really good cookbook for the most basic op amp circuits.
Have fun, and good luck Chris