SOLUTION: The sum of two consecutive numbers is 37. What are the numbers

Two ways to do it. 

1. An easy way that you can do in your head,
but which your teacher won't allow, but it's good
for checking your answer:

Half of 37 is 18.5, so the two numbers are the two
closest whole numbers to 18.5. So the answer: 18 and 19.

2. By algebra:

The smaller = x
The larger = x+1

Their sum = x + (x+1) 

Their sum = 37

  x + (x+1) = 37
  x + x + 1 = 37
     2x + 1 = 37
         2x = 36
          x = 18 = the smaller

The larger = x+1 = 18+1 = 19.

Edwin