document.write( "Question 214887: sum of three consecutive odd integers plus twice the smallest odd interger is 91. Find the integer. \n" ); document.write( "

Algebra.Com's Answer #162328 by drj(1380) $\"\"$ $\"About$

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.\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let n be an odd integer and let n+2 and n+4 be the next two consecutive odd integers.\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let n+n+2+n+4 be the sum of the three consecutive odd integers.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let 2n be twice the smallest odd integer\r
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\n" ); document.write( "\n" ); document.write( "Step 4. n+n+2+n+4+2n=91 as given by the problem statement\r
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\n" ); document.write( "\n" ); document.write( "Step 5. The following will solve the equation in Step 4.\r
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Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

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\n" ); document.write( " YOUR ANSWER\n" ); document.write( "

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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.

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DETAILED EXPLANATION

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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 $\"n%2Bn%2Bhighlight_green%28+6+%29%2Bn%2B2%2An=91\"$ .
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Look at $\"n%2Bn%2Bhighlight_red%28+6+%29%2Bn%2B2%2An=91\"$ .
Moved $\"6\"$ to the right of expression
It becomes $\"n%2Bn%2Bn%2B2%2An%2Bhighlight_green%28+6+%29=91\"$ .
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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 $\"highlight_green%28+%281%2B1%2B1%2B2%29%2An+%29%2B6=91\"$ .
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Look at

.
Added fractions or integers together
It becomes $\"%28highlight_green%28+5+%29%29%2An%2B6=91\"$ .
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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 $\"highlight_green%28+5+%29%2An%2B6=91\"$ .
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Look at $\"5%2An%2B6=highlight_red%28+91+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-91+%29\"$
It becomes $\"5%2An%2B6-highlight_green%28+91+%29=0\"$ .
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Look at $\"5%2An%2Bhighlight_red%28+6+%29-highlight_red%28+91+%29=0\"$ .
Added fractions or integers together
It becomes $\"5%2An%2Bhighlight_green%28+-85+%29=0\"$ .
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Look at $\"5%2An%2Bhighlight_red%28+-85+%29=0\"$ .
Removed extra sign in front of $\"-85\"$
It becomes $\"5%2An-highlight_green%28+85+%29=0\"$ .
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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: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: n=17.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "With n=17, then n+2=19 and n+4=21.\r
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\n" ); document.write( "\n" ); document.write( "Step 6. ANSWER: The integers are 17, 19 and 21 with 17 as the smallest odd integer.\r
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\n" ); document.write( "\n" ); document.write( "I hope the above steps were helpful.\r
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\n" ); document.write( "\n" ); document.write( "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.\r
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\n" ); document.write( "\n" ); document.write( "Good luck in your studies!\r
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\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J\r
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