Question 19: Find x, y, z knowing \(\frac{x}{{ – 4}} = \frac{y}{3} = \frac{z}{7};x + y + z = 24. \)

\(\begin{aligned}&\frac{x}{{ – 4}} = \frac{y}{3} = \frac{z}{7};x + y + z = 24\\&\text {Applying the property of the sequence of equal ratios we have:}\\ &\frac{x}{{ – 4}} = \frac{y}{3} = \frac{z}{7} = \frac{ {x + y + z}}{{\left( { – 4} \right) + 3 + 7}} = \frac{{24}}{6} = 4\\&\frac{x}{{ – 4}} = 4 \Rightarrow x = 4.\left( { – 4} \right) \Rightarrow x = – 16\\&\frac{y}{3} = 4 \Rightarrow y = 4.3 \Rightarrow y = 12 \\&\frac{z}{7} = 4 \Rightarrow z = 4.7 \Rightarrow z = 28\\&\text{So }x=-16, y=12, z=28.\end{aligned} \ )