Question

The sum of two numbers is 30 and their difference is 12.what are the 2 numbers?

Answer 1

The two numbers are `21` and `9`

Explanation:

Let the two numbers be `a` and `b`

The sum of these numbers is `30`
`a + b = 30`

The difference between these numbers is `12`
`a - b = 12`

`color(white)(mmmmmmmm)`―――――――――

I.  You can solve this by logic.

If the two numbers were exactly equal, then they would both be `15`.
`15 + 15 = 30`

But the difference would be `0`, not `12`

So if you lowered `b` by one point, and added that to `a`, then the two numbers would be `16` and `14`, and the difference would be `2`.

So you can see that for every point you subtract from `b` to add to `a`, you increase the distance between them by `2`

So, by logic, you need to subtract `6` points from `b` and add them to `a` to create a difference of `12`

`(15 + 6)` minus `(15 - 6)` gives a difference of `12`
`color(white)(.m)21 color(white)(.....) - color(white)(mmnn)9        =   12`

Answer:
The two numbers are `21` and `9`

`color(white)(mmmmmmmm)`―――――――――

II.  You can solve this by math

These are simultaneous equations, so you can solve them by math.

`color(white)(.)a + b = 30`
`color(white)(.)a - b = 12`
`color(white)()`――――――
`2acolor(lightgray)( + 0)=42`
`color(white)(.)` `a          = 21` `larr` same answer