SOLUTION: sum of three consecutive odd integers plus twice the smallest odd interger is 91. Find the integer.

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Question 214887: sum of three consecutive odd integers plus twice the smallest odd interger is 91. Find the integer.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Sum of three consecutive odd integers plus twice the smallest odd integer is 91. Find the integer.

Step 1. Let n be an odd integer and let n+2 and n+4 be the next two consecutive odd integers.

Step 2. Let n+n+2+n+4 be the sum of the three consecutive odd integers.

Step 3. Let 2n be twice the smallest odd integer

Step 4. n+n+2+n+4+2n=91 as given by the problem statement

Step 5. The following will solve the equation in Step 4.

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


YOUR ANSWER


  • This is an equation! Solutions: n=17.
  • Graphical form: Equation n%2Bn%2B2%2Bn%2B4%2B2n=91 was fully solved.
  • Text form: n+n+2+n+4+2n=91 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+n%2Bn%2B2%2Bn%2B4%2B2n=91+%29
    For tutors: simplify_cartoon( n+n+2+n+4+2n=91 )
  • 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%2B2%2An=91.
Added fractions or integers together
It becomes n%2Bn%2Bhighlight_green%28+6+%29%2Bn%2B2%2An=91.
Look at n%2Bn%2Bhighlight_red%28+6+%29%2Bn%2B2%2An=91.
Moved 6 to the right of expression
It becomes n%2Bn%2Bn%2B2%2An%2Bhighlight_green%28+6+%29=91.
Look at .
Eliminated similar terms highlight_red%28+n+%29,highlight_red%28+n+%29,highlight_red%28+n+%29,highlight_red%28+2%2An+%29 replacing them with highlight_green%28+%281%2B1%2B1%2B2%29%2An+%29
It becomes highlight_green%28+%281%2B1%2B1%2B2%29%2An+%29%2B6=91.
Look at .
Added fractions or integers together
It becomes %28highlight_green%28+5+%29%29%2An%2B6=91.
Look at highlight_red%28+%28highlight_red%28+5+%29%29%2An+%29%2B6=91.
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes highlight_green%28+5+%29%2An%2B6=91.
Look at 5%2An%2B6=highlight_red%28+91+%29.
Moved these terms to the left highlight_green%28+-91+%29
It becomes 5%2An%2B6-highlight_green%28+91+%29=0.
Look at 5%2An%2Bhighlight_red%28+6+%29-highlight_red%28+91+%29=0.
Added fractions or integers together
It becomes 5%2An%2Bhighlight_green%28+-85+%29=0.
Look at 5%2An%2Bhighlight_red%28+-85+%29=0.
Removed extra sign in front of -85
It becomes 5%2An-highlight_green%28+85+%29=0.
Look at highlight_red%28+5%2An-85+%29=0.
Solved linear equation highlight_red%28+5%2An-85=0+%29 equivalent to 5*n-85 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: n=17.

Universal Simplifier and Solver


Done!



With n=17, then n+2=19 and n+4=21.

Step 6. ANSWER: The integers are 17, 19 and 21 with 17 as the smallest odd integer.

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