The sum of two numbers is 99. if three times the smaller number is subtracted from the larger number, the result is 19. find the two numbers.

This is a system of equations. Writing the words in math we get: (we use s as the smaller number and l as the larger one)

l + s = 99
l - 3s = 19

We isolate l in the second equation to get l = 19+3s.  Now we substitute our value of l into the first equation and simplify.
l + s = 99
(19+3s) + s = 99
19 + 4s = 99
4s = 99 - 19
4s = 80
s = 20

Now we know the value for s, we substitute our value for s in the first equation and solve for l.

l + s = 99
l + 20 = 99
l = 99 - 20
l = 79

l = 79 and s = 20. These are our two numbers.