Question 31: Find x, y, z knowing \(\begin{array}{l} \frac{x}{{13}} = \frac{y}{6} = \frac{z}{{17}} \end{array}\) and x+y+z=72.

Applying the property of equal ratios, we have:

\(\begin{array}{l} \frac{x}{{13}} = \frac{y}{6} = \frac{z}{{17}} = \frac{{x + y + z }}{{13 + 6 + 17}} = \frac{{72}}{{36}} = 2\\ \frac{x}{{13}} = 2 \Rightarrow x = 13.2 = 26\\ \ frac{y}{6} = 2 \Rightarrow y = 6.2 = 12\\ \frac{z}{{17}} = 2 \Rightarrow x = 17.2 = 34 \end{array}\)

So x=26; y=12; z=34