Question

Aflati media aritmetica a trei numere, stiind ca doua cate doua au media aritmetica 14,5; 21,4 respectiv 11,5

Answer 1

$\bold{M_a= \frac{x+y+z}{3};} \\ \frac{x+y}{2} =14,5; \\ \frac{y+z}{2} =21,4; \\ \frac{x+z}{2} = 11,5; \\ \Rightarrow x+y=14,5 \cdot 2 \\ \Rightarrow \bold{x+y=29}; \\ \Rightarrow y+z=21,4 \cdot 2 \\ \Rightarrow \bold{y+z=42,8}; \\ \Rightarrow x+z=11,5 \cdot 2 \\ \Rightarrow \bold{x+z=23}; \\ x+y+y+z+x+z=29+42,8+23 \\ x+y+y+z+x+z=94,8 \\ 2x+2y+2z=94,8 \\ 2(x+y+z)=94,8 \\ \Rightarrow x+y+z= \frac{94,8}{2} \\ \Rightarrow \bold{x+y+z=47,4}; \\ \Rightarrow M_a= \frac{47,4}{3}$
$\Rightarrow \boxed{M_a=\boxed{15,8}}.$