Question

The sum of the two numbers is 12. The difference between them is 4. Find the numbers?

Answer 1

The two numbers are `8` and `4`

Explanation:

Call the two numbers `x` and `y`. The first sentence translates to `x+y=12`, while the second sentence translates to `x-y = 4`.

From the second equation we can deduce `x = y+4`. So, the first equation becomes

`y+4+y=12 \iff 2y+4=12 \iff 2y=8 \iff y=4`

Substitute this value for `y` in one of the two equations (say the second) to get

`x-4=4 \iff x=8`