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Philippines Mathematical Olympiad

Algebra Difficulty 5.3 AIME, harder Prove it Philippines

Problem:

The nonzero numbers $x$ , $y$ , and $z$ satisfy the equations
$x y = 2(x + y), \quad y z = 4(y + z), \quad \text{and} \quad x z = 8(x + z)$
Solve for $x$ .

Solution

Solution:

$\dfrac{16}{3}$

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.