document.write( "Question 225514: find three consecutive even integers such that the sum of the first interger is three times the thrid integer is 64 more that the second integer \n" ); document.write( "

Algebra.Com's Answer #168252 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find three consecutive even integers such that the sum of the first integer and three times the third integer is 64 more than the second integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let n be the first even integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let n+2 and n+4 be the next two consecutive even integers.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let 3(n+4) be three times the third integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Let n+3(n+4) be the sum of the first integer and 3 times the third integer\r
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\n" ); document.write( "\n" ); document.write( "Step 5. Let n+2+64=n+66 be 64 more than the second integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 6. Then, n+3(n+4)=n+66 since the sum of the first integer and three times the third integer is 64 more than the second integer\r
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\n" ); document.write( "\n" ); document.write( "Step 7. Solving 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=18.
Graphical form: Equation $\"n%2B3%2A%28n%2B4%29=n%2B66\"$ was fully solved.
Text form: n+3*(n+4)=n+66 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+n%2B3%2A%28n%2B4%29=n%2B66+%29\"$
For tutors: simplify_cartoon( n+3*(n+4)=n+66 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"n%2B3%2A%28n%2B4%29=highlight_red%28+n%2B66+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-n+%29\"$ , $\"highlight_green%28+-66+%29\"$
It becomes $\"n%2B3%2A%28n%2B4%29-highlight_green%28+n+%29-highlight_green%28+66+%29=0\"$ .
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Look at $\"highlight_red%28+n+%29%2B3%2A%28n%2B4%29-highlight_red%28+n+%29-66=0\"$ .
Eliminated similar terms $\"highlight_red%28+n+%29\"$ , $\"highlight_red%28+-n+%29\"$ replacing them with $\"highlight_green%28+%281-1%29%2An+%29\"$
It becomes $\"highlight_green%28+%281-1%29%2An+%29%2B3%2A%28n%2B4%29-66=0\"$ .
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Look at $\"highlight_red%28+%281-1%29%2An+%29%2B3%2A%28n%2B4%29-66=0\"$ .
Since $\"highlight_red%28+%281-1%29%2An+%29\"$ has zero as a factor, it should be replaced with a zero
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Look at $\"0%2B3%2A%28n%2B4%29-66=0\"$ .
Added fractions or integers together
It becomes $\"0%2B3%2A%28n%2B4%29-66=0\"$ .
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Look at $\"highlight_red%28+0+%29%2B3%2A%28n%2B4%29-66=0\"$ .
Remove extraneous zero $\"highlight_red%28+0+%29\"$
It becomes $\"3%2A%28n%2B4%29-66=0\"$ .
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Look at $\"highlight_red%28+3%2A%28n%2B4%29+%29-66=0\"$ .
Expanded term $\"3\"$ by using associative property on $\"%28n%2B4%29\"$
It becomes $\"highlight_green%28+3%2An+%29%2Bhighlight_green%28+3%2A4+%29-66=0\"$ .
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Look at $\"3%2An%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+4+%29-66=0\"$ .
Multiplied numerator integers
It becomes $\"3%2An%2Bhighlight_green%28+12+%29-66=0\"$ .
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Look at $\"3%2An%2Bhighlight_red%28+12+%29-highlight_red%28+66+%29=0\"$ .
Added fractions or integers together
It becomes $\"3%2An%2Bhighlight_green%28+-54+%29=0\"$ .
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Look at $\"3%2An%2Bhighlight_red%28+-54+%29=0\"$ .
Removed extra sign in front of $\"-54\"$
It becomes $\"3%2An-highlight_green%28+54+%29=0\"$ .
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Look at $\"highlight_red%28+3%2An-54+%29=0\"$ .
Solved linear equation $\"highlight_red%28+3%2An-54=0+%29\"$ equivalent to 3*n-54 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: n=18.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "With n=18, then n+2=20 and n+4=22\r
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\n" ); document.write( "\n" ); document.write( "Check equation in Step 6: n+3(n+4)=n+66...18+3*22=18+66 or 84=84...which is a true statement.\r
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\n" ); document.write( "\n" ); document.write( "Step 8 The three consecutive even integers are 18, 20, and 22.\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( "And good luck in your studies!\r
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\n" ); document.write( "\n" ); document.write( "Respectfully,
\n" ); document.write( "Dr J\r
\n" ); document.write( "\n" ); document.write( "http://www.FreedomUniversity.TV \n" ); document.write( "

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