Question 30: Find x; y; z knows \(\begin{array}{l} \frac{x}{2} = \frac{y}{{ – 3}} = \frac{z}{8} \end{array}\) knows xyz =24.

Applying the property of equal ratios, we have:

\(\begin{array}{l} \frac{x}{2} = \frac{y}{{ – 3}} = \frac{z}{8} = \frac{{x – y – z} }{{2 – \left( { – 3} \right) – 8}} = \frac{{24}}{{ – 3}} = – 8\\ \frac{x}{2} = – 8 \ Rightarrow x = 2.\left( { – 8} \right) = – 16\\ \frac{y}{{ – 3}} = – 8 \Rightarrow x = \left( { – 3} \right).\ left( { – 8} \right) = 24\\ \frac{z}{8} = – 8 \Rightarrow x = 8.\left( { – 8} \right) = – 64 \end{array}\)

So x=-16; y=24; z=-64