# How do you find two consecutive even integers whose sum is 126?

Jan 22, 2016

I found $62 \mathmr{and} 64$

#### Explanation:

Let us call our integers:
$2 n$
and
$2 n + 2$
$2 n + \left(2 n + 2\right) = 126$
solve for $n$:
$4 n + 2 = 126$
$4 n = 124$
$n = \frac{124}{4} = 31$
so our numbers will be:
$2 n = 62$
and
$2 n + 2 = 64$

Jan 22, 2016

Two consecutive numbers are: 62 and 64

#### Explanation:

$\textcolor{b l u e}{\text{Method development}}$

2 times any number will give an even number so lets play with some number.

Investigate $2 \left(\textcolor{b r o w n}{5}\right) = 10$ and $2 \left(6\right) = 12$
Looks as though we may have found a mathematical tool that works.

$\textcolor{b r o w n}{\text{I will call the 5 a 'seed number'}}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let the 'seed number be $n$

Then we have

$2 \left(n\right) + 2 \left(n + 1\right) = 126$

$4 n + 2 = 126$

$n = 31$ Remember this is the seed number.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Convert the seed number into the first one needed}}$

$2 n = 2 \times 31 = 62$

Check:

$62 + 64 = 126$ $\textcolor{red}{\text{ It works!}}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Answer}}$

Two consecutive numbers are: 62 and 64