SOLUTION: The sum of four consecutive even integers is 276. Find the four integers

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Question 213852: The sum of four consecutive even integers is 276. Find the four integers
Found 2 solutions by drj, checkley77:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of four consecutive even integers is 276. Find the four integers.

Step 1. Let n be one even integer, n+2 the next consecutive integer, n+4 and n+6 are the next two consecutive integers.

Step 2. So n+n+2+n+4+n+6=276 as given by the problem statement.

Step 3. Solve using the following steps.

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: n=66.
  • Graphical form: Equation n%2Bn%2B2%2Bn%2B4%2Bn%2B6=276 was fully solved.
  • Text form: n+n+2+n+4+n+6=276 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+n%2Bn%2B2%2Bn%2B4%2Bn%2B6=276+%29
    For tutors: simplify_cartoon( n+n+2+n+4+n+6=276 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at n%2Bn%2Bhighlight_red%28+2+%29%2Bn%2Bhighlight_red%28+4+%29%2Bn%2Bhighlight_red%28+6+%29=276.
Added fractions or integers together
It becomes n%2Bn%2Bhighlight_green%28+12+%29%2Bn%2Bn=276.
Look at n%2Bn%2Bhighlight_red%28+12+%29%2Bn%2Bn=276.
Moved 12 to the right of expression
It becomes n%2Bn%2Bn%2Bn%2Bhighlight_green%28+12+%29=276.
Look at .
Eliminated similar terms highlight_red%28+n+%29,highlight_red%28+n+%29,highlight_red%28+n+%29,highlight_red%28+n+%29 replacing them with highlight_green%28+%281%2B1%2B1%2B1%29%2An+%29
It becomes highlight_green%28+%281%2B1%2B1%2B1%29%2An+%29%2B12=276.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+4+%29%29%2An%2B12=276.
Look at highlight_red%28+%28highlight_red%28+4+%29%29%2An+%29%2B12=276.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes highlight_green%28+4+%29%2An%2B12=276.
Look at 4%2An%2B12=highlight_red%28+276+%29.
Moved these terms to the left highlight_green%28+-276+%29
It becomes 4%2An%2B12-highlight_green%28+276+%29=0.
Look at 4%2An%2Bhighlight_red%28+12+%29-highlight_red%28+276+%29=0.
Added fractions or integers together
It becomes 4%2An%2Bhighlight_green%28+-264+%29=0.
Look at 4%2An%2Bhighlight_red%28+-264+%29=0.
Removed extra sign in front of -264
It becomes 4%2An-highlight_green%28+264+%29=0.
Look at highlight_red%28+4%2An-264+%29=0.
Solved linear equation highlight_red%28+4%2An-264=0+%29 equivalent to 4*n-264 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=66.

Universal Simplifier and Solver


Done!



Step 4. So the even integers are 66, 68, 70, 72. These integers add up to 276.

I hope the above steps were helpful.

And good luck in your studies!

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Respectfully,
Dr J

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
x, x+2, x+4 & x+6 are the 4 integers.
x+x+2+x+4+x+6=276
4x=276-12
4x=264
x=264/4
x=66 for the first integer.
66+2=68 second integer.
66+4=70 third integer.
66+6=72 the fourth integer.
Proof:
66+68+70+72=276
276=276