If 48 is added to one-third of a number, the triple of the number is the result. what is the number?

Until we know what it is, let's call the number ' M ', for 'Mystery number'.

                                      The number . . . . M
                   The triple of the number . . . 3M
                   One third of the number . . . . M/3
48 added to one third of the number. . . . M/3 + 48 .

You said that 48 added to one third of the number makes triple the number,
so I can write
                                  M/3 + 48 = 3M
and the rest is easy.

Multiply each side by  3 :    M + 144 = 9M

Subtract  M  from each side:      144 = 8M

Divide each side by  8 :                18 = M

Check:

             Is  M/3 + 48 equal to 3M ?

               (18/3) + 48  ? = ?  3(18)

                   6    + 48  ? = ?  54

                          54       =     54

                                   yay !