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

24.5 and 58.5

they have the difference of 17 and when added together it is 83.

What you can do to solve this question is make a system of equations. 
Doing this, you get:

x+ y = 83
x - y = 17

Now, you can add the two equations together, as y will cancel out, and then solve for x.

You get 2x = 100
Divide by 2 on both sides, to get x = 50.

Then, use the value of x to solve for y using the equations we have already created.
You can use either of the two equations.

In this case, we will use the first one.
Substitute the value of x into the equation, and you get:
50 + y = 83 

Subtract by 50 on both sides, to get y = 33.
The two answers you get are 50 and 33.

However, you should always check your answers by plugging them into the equations.

For the 1st equation: x + y = 83
50 + 33 = 83, Checks out.

For the 2nd equation: x - y = 17
50 - 33 = 17, Checks out.

Now you can be confident of your answers, 50 and 33.
Hope this helped!