document.write( "Question 220978: Find three consecutive odd integers such that the sum of the first, two times the second, and three times the third is 82. \n" ); document.write( "

Algebra.Com's Answer #165775 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find three consecutive odd integers such that the sum of the first, two times the second, and three times the third is 82.\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let n be one odd integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let n+2 and n+4 be the next two odd consecutive integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let 2(n+2) be two times the second.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Let 3(n+4) be three times the third.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. Then n+2(n+2)+3(n+4)=82 since the sum of the first, two times the second, and three times the third is 82\r
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\n" ); document.write( "\n" ); document.write( "Step 6. Solving n+2(n+2)+3(n+4)=82 yields the following steps.\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=11.
Graphical form: Equation $\"n%2B2%2A%28n%2B2%29%2B3%2A%28n%2B4%29=82\"$ was fully solved.
Text form: n+2*(n+2)+3*(n+4)=82 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+n%2B2%2A%28n%2B2%29%2B3%2A%28n%2B4%29=82+%29\"$
For tutors: simplify_cartoon( n+2*(n+2)+3*(n+4)=82 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"n%2B2%2A%28n%2B2%29%2B3%2A%28n%2B4%29=highlight_red%28+82+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-82+%29\"$
It becomes $\"n%2B2%2A%28n%2B2%29%2B3%2A%28n%2B4%29-highlight_green%28+82+%29=0\"$ .
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Look at $\"n%2Bhighlight_red%28+2%2A%28n%2B2%29+%29%2B3%2A%28n%2B4%29-82=0\"$ .
Expanded term $\"2\"$ by using associative property on $\"%28n%2B2%29\"$
It becomes $\"n%2Bhighlight_green%28+2%2An+%29%2Bhighlight_green%28+2%2A2+%29%2B3%2A%28n%2B4%29-82=0\"$ .
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Look at $\"n%2B2%2An%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+2+%29%2B3%2A%28n%2B4%29-82=0\"$ .
Multiplied numerator integers
It becomes $\"n%2B2%2An%2Bhighlight_green%28+4+%29%2B3%2A%28n%2B4%29-82=0\"$ .
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Look at $\"n%2B2%2An%2Bhighlight_red%28+4+%29%2B3%2A%28n%2B4%29-highlight_red%28+82+%29=0\"$ .
Added fractions or integers together
It becomes $\"n%2B2%2An%2Bhighlight_green%28+-78+%29%2B3%2A%28n%2B4%29=0\"$ .
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Look at $\"n%2B2%2An%2Bhighlight_red%28+-78+%29%2B3%2A%28n%2B4%29=0\"$ .
Moved $\"-78\"$ to the right of expression
It becomes $\"n%2B2%2An%2B3%2A%28n%2B4%29%2Bhighlight_green%28+-78+%29=0\"$ .
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Look at $\"n%2B2%2An%2B3%2A%28n%2B4%29%2Bhighlight_red%28+-78+%29=0\"$ .
Removed extra sign in front of $\"-78\"$
It becomes $\"n%2B2%2An%2B3%2A%28n%2B4%29-highlight_green%28+78+%29=0\"$ .
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Look at $\"highlight_red%28+n+%29%2Bhighlight_red%28+2%2An+%29%2B3%2A%28n%2B4%29-78=0\"$ .
Eliminated similar terms $\"highlight_red%28+n+%29\"$ , $\"highlight_red%28+2%2An+%29\"$ replacing them with $\"highlight_green%28+%281%2B2%29%2An+%29\"$
It becomes $\"highlight_green%28+%281%2B2%29%2An+%29%2B3%2A%28n%2B4%29-78=0\"$ .
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Look at $\"%28highlight_red%28+1+%29%2Bhighlight_red%28+2+%29%29%2An%2B3%2A%28n%2B4%29-78=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+3+%29%29%2An%2B3%2A%28n%2B4%29-78=0\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+3+%29%29%2An+%29%2B3%2A%28n%2B4%29-78=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+3+%29\"$
It becomes $\"highlight_green%28+3+%29%2An%2B3%2A%28n%2B4%29-78=0\"$ .
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Look at $\"3%2An%2Bhighlight_red%28+3%2A%28n%2B4%29+%29-78=0\"$ .
Expanded term $\"3\"$ by using associative property on $\"%28n%2B4%29\"$
It becomes $\"3%2An%2Bhighlight_green%28+3%2An+%29%2Bhighlight_green%28+3%2A4+%29-78=0\"$ .
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Look at $\"3%2An%2B3%2An%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+4+%29-78=0\"$ .
Multiplied numerator integers
It becomes $\"3%2An%2B3%2An%2Bhighlight_green%28+12+%29-78=0\"$ .
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Look at $\"3%2An%2B3%2An%2Bhighlight_red%28+12+%29-highlight_red%28+78+%29=0\"$ .
Added fractions or integers together
It becomes $\"3%2An%2B3%2An%2Bhighlight_green%28+-66+%29=0\"$ .
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Look at $\"3%2An%2B3%2An%2Bhighlight_red%28+-66+%29=0\"$ .
Removed extra sign in front of $\"-66\"$
It becomes $\"3%2An%2B3%2An-highlight_green%28+66+%29=0\"$ .
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Look at $\"highlight_red%28+3%2An+%29%2Bhighlight_red%28+3%2An+%29-66=0\"$ .
Eliminated similar terms $\"highlight_red%28+3%2An+%29\"$ , $\"highlight_red%28+3%2An+%29\"$ replacing them with $\"highlight_green%28+%283%2B3%29%2An+%29\"$
It becomes $\"highlight_green%28+%283%2B3%29%2An+%29-66=0\"$ .
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Look at $\"%28highlight_red%28+3+%29%2Bhighlight_red%28+3+%29%29%2An-66=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+6+%29%29%2An-66=0\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+6+%29%29%2An+%29-66=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+6+%29\"$
It becomes $\"highlight_green%28+6+%29%2An-66=0\"$ .
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Look at $\"highlight_red%28+6%2An-66+%29=0\"$ .
Solved linear equation $\"highlight_red%28+6%2An-66=0+%29\"$ equivalent to 6*n-66 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: n=11.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( " $\"n=11\"$ $\"n%2B2=13\"$ and $\"n%2B4=15\"$ \r
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\n" ); document.write( "\n" ); document.write( "Check sum...11+2*13+3*15=11+26+45=82... which is a true statement\r
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\n" ); document.write( "\n" ); document.write( "Step 7. ANSWER: The three consecutive odd integers are 11, 13, and 15.\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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