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.