What two numbers has a sum of 294 and a difference of 64?

Answer 1

179 and 115.

Let the two numbers be x and y. Then:

1. x + y = 294
2. x - y = 64

adding the two equations above give:

x + x + y - y = 294 + 64

⇒ 2x = 358

⇒ x = 179

To find y, substituting for x in (1) above gives:

x + y = 264

⇒ 179 + y = 264

⇒ y = 115

To check the answer, substituting for x and y in (2) above gives:

x - y = 64

⇒ x - y = 179 - 115

= 64 as required.