rate, ratio and proportion

a = x/(2y+4z) = 2y/(x+4z) = 4z/(x+2y)∴ a(2y+4z) = x , a(x+4z) = 2y , a(x+2y) = 4z
⇒
a(2y+4z) + a(x+4z) + a(x+2y) = x + 2y + 4z
a(2x + 4y + 8z) = x + 2y + 4z
2a(x + 2y + 4z) = x + 2y + 4z
(2a - 1) (x + 2y + 4z) = 0
2a - 1 = 0 or x + 2y + 4z = 0
If 2a - 1 = 0 then a = 1/2 ,
or
if x + 2y + 4z = 0 , then x = - 2y - 4z , 2y = - x - 4z , 4z = - x - 2y ,
hence a = - 1 .

謝謝你的教導呀～
彩虹～