SOLUTION: Please help me find 2 consecutive even integers whose sum is 217. The best I got was 106.6 and 108.8 but still fall short. I have these a lot and need to know how to find these w

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Question 213568: Please help me find 2 consecutive even integers whose sum is 217. The best I got was 106.6 and 108.8 but still fall short. I have these a lot and need to know how to find these with a simple math trick or formula. (Algebra 1) Thanks
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find 2 consecutive even integers whose sum is 217.

Step 1. Let n be one odd integer and n+2 be the next consecutive odd integer

Step 2. Note: The sum of two even integers is always even. So in this example there is no solution since 217 is odd.

Step 3. Solve anyway as n+n+2=217 or 2n+2=217

Step 4. Solving yields the following steps:

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


YOUR ANSWER


  • This is an equation! Solutions: n=107.5.
  • Graphical form: Equation 2n%2B2=217 was fully solved.
  • Text form: 2n+2=217 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2n%2B2=217+%29
    For tutors: simplify_cartoon( 2n+2=217 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2An%2B2=highlight_red%28+217+%29.
Moved these terms to the left highlight_green%28+-217+%29
It becomes 2%2An%2B2-highlight_green%28+217+%29=0.
Look at 2%2An%2Bhighlight_red%28+2+%29-highlight_red%28+217+%29=0.
Added fractions or integers together
It becomes 2%2An%2Bhighlight_green%28+-215+%29=0.
Look at 2%2An%2Bhighlight_red%28+-215+%29=0.
Removed extra sign in front of -215
It becomes 2%2An-highlight_green%28+215+%29=0.
Look at highlight_red%28+2%2An-215+%29=0.
Solved linear equation highlight_red%28+2%2An-215=0+%29 equivalent to 2*n-215 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=107.5.

Universal Simplifier and Solver


Done!



Step 5. ANSWER: NO SOLUTION

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J