Question 6: Find x, y, z knowing \(\frac{x}{4} = \frac{y}{9} = \frac{z}{3};x + y + z = 16.\)

\(\begin{aligned}&\frac{x}{4} = \frac{y}{9} = \frac{z}{3};x + y + z = 16\\&\text{Apply property of the sequence of equal ratios we have:}\\ &\frac{x}{4} = \frac{y}{9} = \frac{z}{3} = \frac{{x + y + z }}{{4 + 9 + 3}} = \frac{{16}}{{16}} = 1\\&\frac{x}{4} = 1 \Rightarrow x = 1.4 \Rightarrow x = 4\ \&\frac{y}{9} = 1 \Rightarrow y = 1.9 \Rightarrow y = 9\\&\frac{z}{3} = 1 \Rightarrow z = 1.3 \Rightarrow z = 3\\&\text {So }x=4, y=9, z=3.\end{aligned} \)