SOLUTION: Five brothers, A,B,C,D and E, bought a car for $42000. A paid one third of the sum of the amounts paid by the other brothers. B paid one quarter of the sum of the amounts paid by t

Let a = amount paid by A
    b =             by B
    c =             by C
    d =             by D
    e =             by E.


Then

a =         (1)
b =         (2)
c =         (3)
d =         (4)


Multiply equations: (1) by 3;  (2) by 4; (3) by 5;  and (4) by 6.  The modified system is

3a = b + c + d + e       (5)
4b = a + c + d + e       (6)
5c = a + b + d + e       (7)
6d = a + b + c + e       (8)


Add "a" to both sides of (5).  Add "b" to both sides of (6).  Add "c" to both sides of (7),  Add "d" to both sides of (8).


Use the fact that a + b + c + d + e = 42000.   You will get

4a = 42000  ====>  a =  = 10500.     (9)
5b = 42000  ====>  b =  =  8400.    (10)
6c = 42000  ====>  c =  =  7000.    (11)
7d = 42000  ====>  d =  =  6000.    (12)

Then  a + b + c + d = 10500 + 8400 + 7000 + 6000 = 31900,

and   e = 42000 - 31900 = 10100.


Answer.  E payed 10100.