甲乙丙丁四人去买电视机,夹带的钱是另外三个人所带总数的一半乙带的钱是另外三人所带总钱数的三分之一,丙所带的钱是另外三人所带总数的四分之一,丁带910元,四个人所带的总钱数是多少元?

A甲 B乙 C丙 D丁
A = (B+C+D)/2
B = (A+C+D)/3
C = (A+B+D)/4
D = 910
---------------------D丁带入1.2.3.三个公式
A = (B+C+910)/2
B = (A+C+910)/3
C = (A+B+910)/4
---------------------将C丙带入1.2. 俩公式
A = (B+((A+B+910)/4)+910)/2
B = (A+((A+B+910)/4)+910)/3
---------------------求解公式1.
A = (B+((A+B+910)/4)+910)/2
A = (B+(A/4+B/4+910/4)+910)/2
A = (B+(A/4+B/4+227.5)+910)/2
A = B/2+(A/4+B/4+227.5)/2+910/2
A = B/2+(A/4+B/4+227.5)/2+910/2
A = B/2+A/8+B/8+227.5/2+910/2
A = A/8+B/2+B/8+1137.5/2
A = A/8+4B/8+B/8+1137.5/2
A = A/8+5B/8+1137.5/2
A-A/8 = 5B/8+1137.5/2
(A-A/8)*8 = (5B/8+1137.5/2)*8
A*8-A/8*8 = 5B/8*8+1137.5/2*8
8A-A = 5B+4550
7A = 5B+4550
A = (5B+4550)/7
---------------------求解公式2.
B = (A+((A+B+910)/4)+910)/3
B = (A+(A/4+B/4+910/4)+910)/3
B = (A+(A/4+B/4+227.5)+910)/3
B = (A+(A/4+B/4+227.5)+910)/3
B = A/3+(A/4+B/4+227.5)/3+910/3
B = A/3+A/12+B/12+227.5/3+910/3
B = 4A/12+A/12+B/12+1137.5/3
B = 5A/12+B/12+1137.5/3
12B = (5A/12+B/12+1137.5/3)*12
12B = 5A/12*12+B/12*12+1137.5/3*12
12B = 5A+B+4550
11B = 5A+4550
---------------------将公式1.的结果带入公式2.结果，并求得B
11B = 5((5B+4550)/7)+4550
11B = (25B+4550*5)/7+4550
11B = 25B/7+4550*5/7+4550
11B-25B/7 = 4550*5/7+4550
(11B-25B/7)*7 = (4550*5/7+4550)*7
77B-25B = 4550*5+4550*7
52B = 4550*12
B = 1050
---------------------将结果B的值带入，公式1.的结果。
A = (5*1050+4550)/7
A = 1400
---------------------将AB两个的结果带入公式3.
C = (A+B+910)/4
C = (1400+1050+910)/4
C = 840
---------------------最终结果
A = 1400
B = 1050
C = 840
D = 910
甲 = 1400
乙 = 1050
丙 = 840
丁 = 910
总钱 = 1050+ 1400+ 840+ 910
总钱 = 4200
ps:这个是我的计算习惯。

甲带的钱是总数的1/3
乙带的钱是总数的1/4
丙所带的钱是总数的1/5
∴丁所带的钱是总数的1-1/3-1/4-1/5=1-47/60=13/60
∴总钱数910×13/60=910×60/13=4200元