A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get and B gets two-seventh of what A and C together get. If the amount received by A is $35 more than that received by B, find the total amount shared by A, B and C.
Pick:
A) $ 1360
B) $ 1250
C) $ 1260
D) $ 1270
E) $ 1280

Rationale: "a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 35 a = 35 + b ( 1 ) = = = > c = 105 + 3 b - b = 2 b + 105 = = > 2 b - c = - 105 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 35 = 2.5 b - 35 = = > 2.5 b - c = 35 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 140 b = $ 280 a = $ 315 c = 945 - 280 = $ 665 total amount = 315 + 280 + 665 = $ 1260 answer : c"
Answer: C