Question 10: Find x, y, z knowing \(\frac{x}{6} = \frac{y}{9} = \frac{z}{7};x + y + z = 33.\)

\(\begin{aligned}&\frac{x}{6} = \frac{y}{9} = \frac{z}{7};x + y + z = 33\\&\text{Apply property of the sequence of equal ratios we have:}\\ &\frac{x}{6} = \frac{y}{9} = \frac{z}{7} = \frac{{x + y + z }}{{6 + 9 + 7}} = \frac{{33}}{{22}} = \frac{3}{2}\\&\frac{x}{6} = \frac{3} {2} \Rightarrow x = \frac{3}{2}.6 \Rightarrow x = 9\\&\frac{y}{9} = \frac{3}{2} \Rightarrow y = \frac{3 }{2}.9 \Rightarrow y = \frac{{27}}{2}\\&\frac{z}{7} = \frac{3}{2} \Rightarrow z = \frac{3}{ 2}.7 \Rightarrow z = \frac{{21}}{2}\\&\text{So }x=9, y= \frac{{27}}{2}, z= \frac{{21 }}{2}.\end{aligned} \)