If x,y ,and z are positive real numbers such that x(y+z) = 132, y(z+x) =152 , and z(x+y) = 180, then xyz is
Choose the most appropriate option
A) 40
B) 60
C) 160
D) 100
E) 120

Rationale: xy + xz = 132 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 ) yz + yx = 152 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ) xz + zy = 180 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3 ) re - writing equation 3 as follows : xz + zy = 152 + 28 xz + zy = yz + yx + 28 xz = yx + 28 . . . . . . . . . . . . . . . ( 4 ) adding ( 1 ) ( 4 ) 2 xz = 160 xz = 80 xyz has to be multiple of 80 , only 160 fits in answer = c
Answer: C