Question 3: Find three numbers x, y, z knowing that x, y, z are proportional to 11;-3;-4 and their sum is 8.

\(\begin{aligned}&\text{Let x, y, z be the 3 numbers to find.According to the problem we have:}\\&\frac{x}{{11}} = \frac{y}{ { – 3}} = \frac{z}{{ – 4}};x + y + z = 8\\&\text{Applying the property of equal ratios we have:}\\ &\frac{ x}{{11}} = \frac{y}{{ – 3}} = \frac{z}{{ – 4}} = \frac{{x + y + z}}{{11 + \left( { – 3} \right) + \left( { – 4} \right)}} = \frac{8}{4} = 2\\&\frac{x}{{11}} = 2 \Rightarrow x = 2.11 \Rightarrow x = 22\\&\frac{y}{{ – 3}} = 2 \Rightarrow y = 2.\left( { – 3} \right) \Rightarrow y = – 6\\&\frac{ z}{-4} = 2 \Rightarrow z = 2.(-4) \Rightarrow z = -8\\&\text{So the 3 numbers to look up are 22;-6;-8}\end{aligned, respectively. } \)