Question

The sum of two numbers is 16 and their difference is 20. What are the two numbers?

how do I figure this out?

Answer 1

`18 and -2`

Explanation:

Let the numbers be `m and n`

The sum of the numbers is 16 `-> m+n =16`

Their difference is 20 `-> m-n=20`

Thus we have a system of simultaneous equations:

`m+n =16` [A]

`m-n =20` [B]

[A]+[B] `-> 2m =36`

`:. m=18`

`m=18` in [B] `-> 18-n =20`

`n=18-20 =-2`

Hence our two numbers are `18 and -2`

Check:
`18+(-2) = 18-2=16`
`18-(-2) = 18+2 =20`

Answer 2

The numbers are `18` and `-2`.

Explanation:

Let x be the first number and let y be the second number.
`x + y =16`
`x-y = 20`
After adding the two equations:
`2x = 36`
`x = 18`
Substituting 18 for x to find y:
`18 + y=16`
`y = -2`

Answer 3

The numbers are 18 and -2.
You should set up equations to solve them.

Explanation:

The ones I did were:
`a-b=20`, which represents that the difference was `20`.
`a+b=16`, which represents that the sum of the two numbers is 16.
You should then isolate a variable(I isolated `a`).
`=>` `a=16-b` and `a=20+b`, because `a` must equal `a`.
So, `16-b=20+b`
Add `-b` to `b` `=>` `16=2b+20`
Subtract `20` from both sides `=>` `2b=-4`
Divide by `2` => `b=-2`
Since `b=-2`, plug `b` into an equation.
`=>` `a+(-2)=16` `=>` `a-2=16`
Add `2` to both sides `=>` `a=18`
`b=-2`, `a=18`