How do you find three consecutive even integers whose sum is 244?

2 Answers
Jun 13, 2015

There are no three consecutive even integers whose sum is 244.

Jun 13, 2015

Answer:

To attempt to find three such integers, you could solve #244 = n+(n+2)+(n+4)# and find that the resulting #n# isn't an integer. So there are no such three consecutive even integers.

Explanation:

If there are three such integers then they are of the form #n#, #n+2# and #n+4#.

Then we have:

#244 = n + (n+2) + (n+4) = 3n+6#

Subtract #6# from both sides to get:

#238 = 3n#

Divide both sides by #3# to get:

#n = 79.dot(3)dot(3)#

which is not an integer, let alone an even one.

So there is no solution.