Calculations for building a mixer circuit
It should be possible to do this with 3 resistors:



The gain from V1 to OUT is a resistor divider with R1 as the top leg and the parallel combination of R2 and R3 as the bottom leg:

&nbsp;G1 = (R2//R3) / (R1 + R2//R3) = 1/2

Similarly, you can write the equation for the gain from V2 to the output:

&nbsp;G2 = (R1//R3) / (R2 + R1//R3) = 1/6

Now you have two equations and three unknowns.  That should tell you the problem is underconstrained.  With a little thought you should realize that if you have one set of resistors that meet the requirements, you can easily find others by multiplying all the resistors by the same constant.  In other words, all that matters is the ratio of the resistors as the problem is stated.  The absolute value effects apparent impedances, but those weren't specified.

To get the third constraint, you can simply pick a fixed value for one of the resistors.  For example, decide R3 is 1 &Omega;, then solve for the remaining two values.  If you later decided you would rather R3 were 1 k&Omega;, then you can multiply all the values by 1k.

So the third equation is:

&nbsp;R3 = 1 k&Omega;

Now you have three independent equations and three unknowns.  The rest is simple algebra.  This is your problem, so I'll leave that as a exercise for you.