Question

The sum of two numbers is 40. The larger number is 8 more than the smaller number. What are the numbers?

Answer 1

Our smaller number is `16`, and our larger number is `24`.

Explanation:

Let us say that the smaller number is `x`. Now, since the larger number is `8` more than the smaller number, it is `x+8`.

From the question, we know that their sum is `40`. We add the smaller number `x` to the larger number `x+8` to get `x+x+8=2x+8`. This value is equal to `40`.

Therefore, `2x+8=40`. In order to solve this equation, we have to remember that we can do anything to one side of the equation provided that we do the exact same thing to the other side.

Suppose that we subtract `8` from both sides: `2x+8-8=40-8`. Simplifying, we get `2x=32`.

Now, suppose we divide both sides by `2`: `2x-:2=32-:2`. Simplifying, we get `x=16`.

We have our smaller number. Looking back, we said that the larger number is `8` more than the smaller number. Eight more than `16` is `24`.

Our smaller number is `16`, and our larger number is `24`. They do add up to `40` (since `16`+`24`=`40`).

Answer 2

The smaller number is `16`.
The larger number is `24`.

Explanation:

Let `x` be the first and smaller number, and let `y` be the second and larger number.

The two equations are:
`x+y=40`

`y=8+x`

Substituting the second equation into the first:
`x+(8+x)=40`

`2x+8=40`

`2x=32`

Smaller number: `x=16`

`y=8+(16)`

Larger number: `y=24`