Question

The sum of two numbers is 27. The larger number is 6 more than twice the smaller number. What are the numbers?

Answer 1

`7` and `20`.

Explanation:

Okay, I'm going to put these as an equation, to make things a bit easier for you.

Let `x` be the bigger number and let `y` be the smaller number.

`x + y = 27`

`x = 2y +6`

Once you see those, it's quite clear that this is a simple substitution problem. So, let's solve for `y` first:

`2y+6+y=27`

And then let's substitute it in for the first number:

`3y +6-6=27-6`

`3y= 21`

`y=7`

And then to solve for `x`:

`x +7=27`

`x+7-7=27-7`

`x=20`

Answer 2

The smaller number is `7`, the larger is `20`

Explanation:

This problem can be solved using just one variable.

Let the smaller number be `x`.

If the two numbers add to 27, then the numbers can be written as:

`x and (27-x)`

Twice the small number: `2x`
Six more than twice the smaller number: `2x +6`

That is the same as (=) the bigger number:

`2x+6 = 27-x`

`2x+x = 27-6`

`3x = 21`

`x =7`

If the smaller number is `7`, the larger is `20`

Check: `2 xx 7 +6 = 20`