Question

The difference of two numbers is 3. Their sum is 13. How do you find the numbers?

Answer 1

The two numbers are `8` and `5`.

Explanation:

Consider the two numbers as `x` and `y`. From the given data, we write:

`x-y=3`
`x+y=13`

From the first equation, we determine a value for `x`.

`x-y=3`

Add `y` to both sides.

`x=y+3`

In the second equation, substitute `x` with `color(red)((y+3))`.

`x+y=13`

`color(red)((y+3))+y=13`

Open the brackets and simplify.

`color(red)(y+3)+y=13`

`2y+3=13`

Subtract `3` from each side.

`2y=10`

Divide both sides by `2`.

`y=5`

In the first equation, substitute `y` with `color(blue)(5)`.

`x-y=3`

`x-color(blue)(5)=3`

Add `5` to each side.

`x=8`