If a,b ,and c are positive real numbers such that a(b+c) = 152, b(c+a) =162 , and c(a+b) = 170, then abc is  Choose the correct choice from the following answers.
A) 672
B) 688
C) 704
D) 720
E) 750

Rationale: ab + bc = 152 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 ) bc + ba = 162 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ) ac + ab = 170 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3 ) re - writing equation 3 as follows : ac + cb = 162 + 8 ac + cb = bc + ba + 8 ac = ba + 8 . . . . . . . . . . . . . . . ( 4 ) adding ( 1 ) ( 4 ) 2 ac = 160 ac = 80 abc has to be multiple of 80 , only 720 fits in answer = d
Answer: D