Question 20
If $x,$ $y,$ and $z$ are positive numbers satisfying $$
x + \frac{1}{y} = 4,
$$ $$
y + \frac{1}{z} = 1,
$$ and $$
z + \frac{1}{x} = \frac{7}{3},
$$ then what is $xyz?$
x + \frac{1}{y} = 4,
$$ $$
y + \frac{1}{z} = 1,
$$ and $$
z + \frac{1}{x} = \frac{7}{3},
$$ then what is $xyz?$