What two numbers add up to 200 and have a difference of 84?

Answer 1

(200 - 84)/2 = 58

and

(200 + 84)/2 = 142

For futher explication, see below.

Call the lesser and greater of the two required numbers l and g respectively. the, from the problem statement, l + g = 200 and g - l = 84. Rearrange the first of these equations to give g = 200 - l and substitute this expression into the second of the equations to result in g - (200 - g) = 84, or 2g - 200 = 84, or g 284/2 or 142. l is then (200 - 142) or 58.