Question 23: Find x, y, z knowing \(\frac{x}{2} = \frac{y}{{ – 5}} = \frac{z}{7};x + y + z = 20\ )

\(\begin{aligned}&\frac{x}{2} = \frac{y}{{ – 5}} = \frac{z}{7};x + y + z = 20\\&\text {Applying the property of the sequence of equal ratios, we have:}\\ &\frac{x}{2} = \frac{y}{{ – 5}} = \frac{z}{7} = \frac{ {x + y + z}}{{2 + \left( { – 5} \right) + 7}} = \frac{{20}}{4} = 5\\&\frac{x}{2} = 5 \Rightarrow x = 2.5 \Rightarrow x = 10\\&\frac{y}{{ – 5}} = 5 \Rightarrow y = 5.\left( { – 5} \right) \Rightarrow y = – 25 \\&\frac{z}{7} = 5 \Rightarrow z = 5.7 \Rightarrow z = 35\\&\text{So}x=10, y=-25, z=35.\end{aligned} \ )