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

2 Answers
Gió
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#

Tony B
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

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