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

2 Answers
Jan 22, 2016

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

Jan 22, 2016

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