Three boxes each contain an equal number of hockey pucks. Each puck is either black or gold. All 40 of the black pucks and exactly $\frac{1}{7}$ of the gold pucks are contained in one of the three boxes. Determine the total number of gold hockey pucks.
Suppose that $g$ is the number of gold pucks. We are told that the first box contains all 40 black pucks and exactly $\frac{1}{7}$ of the gold pucks, so it contains $40+\frac{1}{7} g$ pucks.

The remaining two boxes must contain the remaining $\frac{6}{7} g$ gold pucks and no black pucks.

We are told that each box contains the same number of pucks.

Since each of the second and third boxes contains the same number of pucks, then each must contain $\frac{1}{2} \times \frac{6}{7} g=\frac{3}{7} g$ gold pucks.

Since the first and second boxes contain the same number of pucks, then $40+\frac{1}{7} g=\frac{3}{7} g$ or $\frac{2}{7} g=40$, and so $g=\frac{7}{2}(40)=140$.

Therefore, there are 140 gold hockey pucks in total.

(We can verify that if there are 140 gold pucks, then the first box contains 40 black pucks and 20 gold pucks (or 60 pucks in total), and the remaining two boxes each contain half of the remaining 120 gold pucks, or 60 gold pucks each in total.)

ANSWER: 140