Divide $106 among Shelley, Veronica, Christy, and Ruth so that Shelley and Veronica together have $56, Shelley and Christy together have $59, and Shelley and Ruth together have $43.
Shelley gets $26.
Veronica gets $30.
Christy gets $33.
Ruth gets $17.
One way to get it: S + V + C + R = 106.
But S + V = 56,
S + C = 59, and
S + R = 43.
Substituting V, C, and R in terms of S and simplifying, we get 2S = 52, so S = 26, and it’s easy from here.
For students who don’t have a grip on algebra, here is a nice question that can lead to the solution without using algebra: Notice that 56 + 59 + 43 = 158, which is not 106 — why not? Someone will notice that Shelley’s share has been included 3 times, so 158 – 106 = 52 must be the 2 extra Shelley shares. The solution follows easily.