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

Answer 1

Julia Adams

Two consecutive numbers are: 62 and 64

#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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Answer 2

Eli Assouline

I found #62 and 64#

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#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.