數學知識交流---平均值(2)

A, B, C, D, E = 104 (average)
( A + B + C + D + E ) / 5 = 104
A + B + C + D + E = 520 ----------(1)
B, 2C, 3D, 4E, 5A = 518 (average)
( B + 2C + 3D + 4E + 5A ) / 5 = 518
B + 2C + 3D + 4E + 5A = 2590 --(2)
(A+B), (B+5), (C+D), (2E-D), (D-B-E), (E) = 105 (average)
(A+B+B+5+C+D+2E-D+D-B-E+E) / 6 = 105
A + B + C + D + 2E = 625 ------(3)
(E-1),(D-2),(C-3),(B-A),-4 = 87 (average)
(E-1+D-2+C-3+B-A-4) / 5 = 87
-A + B + C + D + E = 445 ---------(4)
U = A + B + C + D + E ------------(5)
U, (A+B-C+E-D) = 398 (average)
( U + A + B - C + E - D ) / 2 = 398
U + A + B - C - D + E = 796 -------(6)
(3) - (1)，得：
E = 105
(1) - (4)，得：
2A = 75
A = 37.5
把(5)代入(6)，得：
A+B+C+D+E+A+B-C-D+E = 796
2A+2B+2E = 796
75 + 2B + 210 = 796
B = 255.5
把A = 37.5, B = 255.5, E = 105代入(1)和(2)，得：
C + D = 122
2C + 2D = 244 ----(7)
255.5 + 2C + 3D + 420 + 187.5 = 2590
2C + 3D = 1727 ---(8)
(8) - (7)，得：
D = 1483
C = 122 - 1483 = -1361
把(1)代入(6)，得：
U = 520


2011-07-19 22:43:52 補充：
檢驗：
( 37.5 + 255.5 - 1361+ 1483 + 105 ) / 5 = 104
( 255.5 - 2722 + 4449 + 420 + 187.5 ) / 5 = 518
( 293 + 260.5 + 122 - 1273 + 1122.5 + 105 ) / 6 = 105
( 104 + 1481 - 1364 + 218 - 4 ) / 5 = 87
520 = 37.5 + 255.5 - 1361 + 1483 + 105
( 520 + 276 ) / 2 = 398
correct!

2011-07-19 22:43:58 補充：
A = 37.5, B = 255.5, C = -1361, D = 1483, E = 105, U = 520