assume that the fsmaller number =S and the larger number is=L

then, S+L= 53....... (1)

3 times the smaller number = 19 more than the larger number

==> 3 S = 19 + L ........ (2)

Now, combining equation (1) and (2) we have:

S+L = 53

3S = 19  + L ==> L = 3S -19

substitute in eqution (1),

 S + (3S- 19) = 53

 4S - 19 = 53

4S = 72     divide by 4

S = 72/4 = 18

and L = 3(18)- 19 = 35

The larger number is 35 and the smaller number is 18.  Here is how to find this.

Let X be the smaller number and Y be the larger.

x + y = 53

3x = y + 19

Let us solve for y in the first equation.

y = 53 -x

Then let us substitute that for y in the second equation.

3x = 53 - x + 19

3x = -x + 72

4x = 72

x = 18

If x = 18

18 + y = 53

y = 35