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# The sum of three consecutive even integers is 108. What is the largest number?

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im taking a summer class and this question has me stumped i might just be over thinking it can anyone help me?

Guest Jul 3, 2014

#3
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Thanks, Alan....I gave him some points anyway.....

Here's a slightly "non-mathematical" way to do this.....

Divide 108 by 3 = 36

So, 36 + 36 + 36 = 108   Subtract 2 from the first 36 and add 2 to the last

34 + 36 + 38

CPhill  Jul 3, 2014
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#1
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represent the numbers as n, n+1, and n+2 as this guarantees that they are consecutive.

Then n+(n+1)+(n+2)=108

3n+3=108

3n=105

n=35

They would love you to answer 35 but thats incorrect because they asked for the LARGEST number.  That is n+2 which is 37

jboy314  Jul 3, 2014
#2
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jboy314 has answered a slightly different question from the one asked; forgetting that all even numbers were specified!

With all even numbers we have n + (n+2) + (n+4) = 108 or 3n + 6 = 108, so 3n = 102 and n = 34.

The largest number is therefore 34 + 4 = 38.

Alan  Jul 3, 2014
#3
+81014
+10

Thanks, Alan....I gave him some points anyway.....

Here's a slightly "non-mathematical" way to do this.....

Divide 108 by 3 = 36

So, 36 + 36 + 36 = 108   Subtract 2 from the first 36 and add 2 to the last

34 + 36 + 38

CPhill  Jul 3, 2014
#4
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It should be noted that jboy314 didn't notice the word "even"

this is a very common oversite.  I did it myself not that long ago.

Alan and Jboy's answers are the most common but I do like Chris's take on the problem.

Melody  Jul 5, 2014

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