SOLUTION: what is the greatest of 5 consecutive even integers if the sum of these integers equals 120? i don't really understand what the question is akin me and i don't know how to

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: what is the greatest of 5 consecutive even integers if the sum of these integers equals 120? i don't really understand what the question is akin me and i don't know how to      Log On


   

Question 827785: what is the greatest of 5 consecutive even integers if the sum of these integers equals 120?



i don't really understand what the question is akin me and i don't know how to do it
this is our sat problem of the week and owe haven't learned this yet

thanks you! :)
Answer by KMST(5347) About Me  (Show Source):
You can put this solution on YOUR website!
WITH PENCIL AND PAPER (SLOW):
If I was going to use pencil and paper, I would start by assigning a variable name or an expression to one of those integers.
An even integer can be called n or 2n .
IF you start with
2n= the greatest of the 5 consecutive even integers, the other even integers are
2n-2 , 2n-4 , 2n-6 , and 2n-8 .
The sum of those 5 consecutive even integers is
2n%2B%282n-2%29%2B%282n-4%29%2B%282n-6%29%2B%282n-8%29=120
Solving:
2n%2B%282n-2%29%2B%282n-4%29%2B%282n-6%29%2B%282n-8%29=120
2n%2B2n-2%2B2n-4%2B2n-6%2B2n-8=120
2n%2B2n%2B2n%2B2n%2B2n=120%2B2%2B4%2B6%2B8
10n=140
n=140%2F10
n=14
2n=2%2A14
highlight%282n=28%29

FASTER MENTAL MATH:
(I can think my way to the solution fast, but explaining it takes time).
I know that consecutive integers are evenly spaced.
(Each one is 2 more than the one before; they are an arithmetic sequence).
For an arithmetic sequence, if I have 5 of the terms (or 7 of them, or 9, or any odd number of them), the middle term is the average and the median.
So the sum of 5 consecutive even integers is 5 times the middle integer (the third integer).
So 5 times that integer is 120, meaning that the middle integer is 24, and the next to even integers are 26 and highlight%2828%29 .
The greatest of the 5 even integers is highlight%2828%29 .