River City Circuits Corp's consultant - the inestimable R. J. Conque - has been working on a product for measuring temperature in their plant.  They want to measure temperature at several points and compute the average.  However, they only have one A/D input port on the computer they want to use, so they would be interested in a circuit that averaged all the measurements into one voltage proportional to the average.

        They are using temperature sensors the produce a voltage that is proportional to the temperature the sensor is exposed to.  In particular, V = 0.01*Temp, when the temperature is measured in Fahrenheit.

        Conque suggests this circuit, and suggestst that it can take the average of N voltages if the resistors are chosen properly.  RC3 will be satisfied if you can tell them if the circuit will work as desired for three (3) voltage sources, so you can consider N = 3, and forget the dotted lines that imply that there are more resistors in the drawing below.  Now, answer this question:

• Is it possible to choose resistance values, R₁, R₂ and R₃ in this circuit so that the output voltage, Vout, is proportional to the average of the three voltages, V₁, V₂ and V₃?  You need to answer the question and give a convincing explanation of your answer.