Question 24: Find x, y, z knowing \(\frac{x}{1} = \frac{y}{3} = \frac{z}{4};x + y + z = 24\)

\(\begin{aligned}&\frac{x}{1} = \frac{y}{3} = \frac{z}{4};x + y + z = 24\\&\text{Apply property of the sequence of equal ratios we have:}\\ &\frac{x}{1} = \frac{y}{3} = \frac{z}{4} = \frac{{x + y + z }}{{1 + 3 + 4}} = \frac{{24}}{8} = 3\\&\frac{x}{1} = 3 \Rightarrow x = 3\\&\frac{y} {3} = 3 \Rightarrow y = 3.3 \Rightarrow y = 9\\&\frac{z}{4} = 3 \Rightarrow z = 3.4 \Rightarrow z = 12\\&\text{So }x=3, y=9, z=12.\end{aligned} \)