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

May 6, 2017

$7$ 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.

$x + y = 27$

$x = 2 y + 6$

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

$2 y + 6 + y = 27$

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

$3 y + 6 - 6 = 27 - 6$

$3 y = 21$

$y = 7$

And then to solve for $x$:

$x + 7 = 27$

$x + 7 - 7 = 27 - 7$

$x = 20$

May 6, 2017

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:

$x \mathmr{and} \left(27 - x\right)$

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

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

$2 x + 6 = 27 - x$

$2 x + x = 27 - 6$

$3 x = 21$

$x = 7$

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

Check: $2 \times 7 + 6 = 20$