There are 2 numbers whose sum is 53. 3 times the smaller number is equal to 19 more than the larger number. Which are the numbers?

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