Question 7: Find x, y, z know \(\frac{x}{{11}} = \frac{y}{{ – 3}} = \frac{z}{{ – 4}};x + y + z = 8.\)

\(\begin{aligned}&\frac{x}{{11}} = \frac{y}{{ – 3}} = \frac{z}{{ – 4}};x + y + z = 8 \\&\text{Applying the property of the sequence of equal ratios we have:}\\ &\frac{x}{{11}} = \frac{y}{{ – 3}} = \frac{z} {{ – 4}} = \frac{{x + y + z}}{{11 + \left( { – 3} \right) + \left( { – 4} \right)}} = \frac{8 }{4} = 2\\&\frac{x}{{11}} = 2 \Rightarrow x = 2.11 \Rightarrow x = 22\\&\frac{y}{{ – 3}} = 2 \Rightarrow y = 2.\left( { – 3} \right) \Rightarrow y = – 6\\&\frac{z}{-4} = 2 \Rightarrow z = 2.(-4) \Rightarrow z = -8\ \&\text{So }x=22, y=-6, z=-8.\end{aligned} \)