Question 13: Find x, y, z knowing \(\frac{x}{4} = \frac{y}{9} = \frac{z}{5};x + y + z = 9.\)

\(\begin{aligned}&\frac{x}{4} = \frac{y}{9} = \frac{z}{5};x + y + z = 9\\&\text{Apply property of the sequence of equal ratios we have:}\\ &\frac{x}{4} = \frac{y}{9} = \frac{z}{5} = \frac{{x + y + z }}{{4 + 9 + 5}} = \frac{9}{{18}} = \frac{1}{2}\\&\frac{x}{4} = \frac{1}{2 } \Rightarrow x = \frac{1}{2}.4 \Rightarrow x = 2\\&\frac{y}{9} = \frac{1}{2} \Rightarrow y = \frac{1}{ 2}.9 \Rightarrow y = \frac{1}{{18}}\\&\frac{z}{5} = \frac{1}{2} \Rightarrow z = \frac{1}{2} .5 \Rightarrow z = \frac{1}{{10}}\\&\text{So }x=2, y= \frac{1}{{18}}, z= \frac{1}{{ 10}}.\end{aligned} \)