SOLUTION: 5 years ago carlos age was 7 times of tom's age but after 3 years carlos age will be 4 times of tom's age. calculate their ages ?

C - 5 = 7*(T-5)     (1)     (5 years ago . . . )
C + 3 = 4*(T+3)     (2)     (in 3 years . . . )


From (1), express  C = 7*(T-5) + 5 = 7T -35 + 5 = 7T -30   and substitute it into eq(2).  You will get


(7T - 30) + 3 = 4*(T+3)

7T - 27 = 4T + 12

3T = 12 + 27 = 39  ====>  T =  = 13.


Answer.  T = 13,  C = 7T - 30 = 7*13-30 = 91-30 = 61.