1550.11 – Shelley, Veronica, Christy, and Ruth

Shelley, Veronica, Christy, and Ruth earned a total of $106 by selling tickets to their turtle race. Shelley and Veronica would like to buy two pounds of blackworms to feed their turtles' offspring, come late summer. Shelley and Christy will donate to the Red-Eared Slider Anarchic Collective. Shelley and Ruth will each spend part of their share on fine alpaca yarn to knit sweaters for their turtles.

Divide the $106 so that Shelley and Veronica together have $56, Shelley and Christy together have $59, and Shelley and Ruth together have $43. How much money does each person get? (You can do this without knowing any algebra.)

Solution

Shelley gets $26, Veronica gets $30, Christy gets $33, and Ruth gets $17.

Their turtles will be so happy. One way to solve this problem is:

$S + V + C + R = 106$

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 so on.

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 along...