Question 1059554
Let:
   S = Sam's age
   T = Tonton's age
   R = Ramon's age
—
  S<R  and  S>T   (given)
   This info implies  T<S<R so:

   T=youngest age
   S=T+1
   R=T+2
—
Let M = mother's age
    M = 3(T+1)    ("Thrice as old as Sam."  Recall S=T+1)
    M = 2(T+2)+14  ("14 yrs older than twice as old as Ramon."  Recall R=T+2)
—
Now we can solve for T (2 eqns, 2 unknowns).  M is easily eliminated from the above two eqns by setting the two right hand sides equal to each other:

  {{{ 3(T+1) = 2(T+2)+14  }}}
Now solve for T:
  {{{ 3T + 3 = (2T+4) + 14 }}}
  {{{ T = 15 }}}

—

Answer:
   Tonton is 15
   Sam is 16
   Ramon is 17   

—

Check (using the age relations of Sam's mother):
   3*16 = 48 
    14+2*17 = 14+34 = 48