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
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