Question

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

Answer 1

I found `62 and 64`

Explanation:

Let us call our integers:
`2n`
and
`2n+2`
and use your condition as:
`2n+(2n+2)=126`
solve for `n`:
`4n+2=126`
`4n=124`
`n=124/4=31`
so our numbers will be:
`2n=62`
and
`2n+2=64`

Answer 2

Two consecutive numbers are: 62 and 64

Explanation:

`color(blue)("Method development")`

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

Investigate `2(color(brown)(5))=10` and `2(6)=12`
Looks as though we may have found a mathematical tool that works.

`color(brown)("I will call the 5 a 'seed number'")`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let the 'seed number be `n`

Then we have

`2(n)+2(n+1)=126`

`4n+2=126`

`n= 31` Remember this is the seed number.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Convert the seed number into the first one needed")`

`2n=2xx31=62`

Check:

`62+64=126` `color(red)(" It works!")`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answer")`

Two consecutive numbers are: 62 and 64