Question

dada 6 /x 21 /y 15/z haya los valores de x, y, z si x+y+z=56

Answer 1

Dada 6 /x 21 /y 15/z haya los valores de x, y, z si x+y+z=56

Hola!!!

Usamos la Proporción para colocar todo en función de una variable, entonces

$\dfrac{6}{x}=\dfrac{21}{y}=\dfrac{15}{z}\qquad\qquad\qquad x+y+z=56\\\\\\\dfrac{6}{x}=\dfrac{21}{y}\to 6y=21x\to \boxed{y=\frac{21}{6}x}\\\\\\\dfrac{6}{x}=\dfrac{15}{z}\to 6z=15x\to \boxed{z=\frac{15}{6}z}\\\\Entonces\\\\x+y+z=56\qquad\qquad\qquadreemplazamos\\\\\\x+\dfrac{21}{6}x+\dfrac{15}{6}x= 56\\\\\\\dfrac{6x+21x+15x}{6}=56\\\\\\ 42x=56*6\\\\42x=336\quad\tox=\dfrac{336}{42}\qquad\to \boxed{x=8}\\\\\\y=\dfrac{21}{6}x\to y=\dfrac{21}{6}.8\to\boxed{y=28}$

$z=\dfrac{15}{6}x\to z=\dfrac{15}{6}.8\to\boxed{z=20}\\\\ Verificamos\\\\x+y+z=56\\\\8+28+20= 56\\\\56=56$

Espero que te sirva, salu2!!!!