Two numbers total 83 and have a difference of 17 find the two numbers

[math_celebrity]

Let the numbers be x and y. Set up our givens:

1. x + y = 83
2. x - y = 17

Add equation (1) to equation (2)
x + x + y - y = 83 + 17

The y-terms cancel out:
2x = 100

Divide each side by 2:
2x/2= 100/2
x = 50

Plug x = 50 into equation (1)
50 + y = 83

Subtract 50 from each side:
50 - 50 + y = 83 - 50

Cancel the 50 on the left side:
y = 33

So our two numbers (x, y) = (33, 50)