Jolene invests her savings in two bank accounts, one paying 6% and the other paying 12% interest per year.
She puts twice as much in the lower-yielding account because it is less risky.
If she earned $6936 of total interest for the year, how much was invested in each account?

I can use variables to represent the coordinates of the vertices for a general triangle, ∆ABC. Then I can calculate the midpoints of the sides in terms of those variables. Using the point-slope formula for the equation of a straight line, I can build the symbolic equations for the three medians, AE, BF, and CD. I can solve for the point of intersection for two of the medians, AE and BF, for example. Finally, I can prove the lines (i.e., medians) concurrent if the point I found also satisfies the equation of the line for CD.