Question 22: Find x, y, z knowing \(\frac{x}{3} = \frac{y}{5} = \frac{z}{{ – 4}};x + y + z = 7. \)

\(\begin{aligned}&\frac{x}{3} = \frac{y}{5} = \frac{z}{{ – 4}};x + y + z = 7\\&\text {Applying the property of the sequence of equal ratios, we have:}\\ &\frac{x}{3} = \frac{y}{5} = \frac{z}{{ – 4}} = \frac{ {x + y + z}}{{3 + 5 + \left( { – 4} \right)}} = \frac{7}{4}\\&\frac{x}{3} = \frac{ 7}{4} \Rightarrow x = \frac{7}{4}.3 \Rightarrow x = \frac{{21}}{4}\\&\frac{y}{5} = \frac{7} {4} \Rightarrow y = \frac{7}{4}.5 \Rightarrow y = \frac{{35}}{4}\\&\frac{z}{{ – 4}} = \frac{7 }{4} \Rightarrow z = \frac{7}{4}.\left( { – 4} \right) \Rightarrow z = – 7\\&\text{So}x= \frac{21}{4 }, y= \frac{35}{4}, z=-7.\end{aligned} \)