document.write( "Question 222441: find three consecutive whole numbers such that twice the sum of the two smallest numbers is 10 more than three times the largest number \n" ); document.write( "

Algebra.Com's Answer #166587 by drj(1380) $\"\"$ $\"About$

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Find three consecutive whole numbers such that twice the sum of the two smallest numbers is 10 more than three times the largest number.\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let n be an integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let n+1 and n+2 be the next two consecutive integers.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let n+n+1=2n+1 be the sum of the two smallest integers.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Let 2(2n+1) be twice the sum of the two smallest integers.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. Let 3(n+2) be three times the largest number\r
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\n" ); document.write( "\n" ); document.write( "Step 6. Then using Steps 3 and 4, 2(2n+1)=3(n+2)+10 since twice the sum of the two smallest numbers is 10 more than three times the largest number.\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=14.
Graphical form: Equation $\"2%2A%282n%2B1%29=3%2A%28n%2B2%29%2B10\"$ was fully solved.
Text form: 2*(2n+1)=3*(n+2)+10 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+2%2A%282n%2B1%29=3%2A%28n%2B2%29%2B10+%29\"$
For tutors: simplify_cartoon( 2*(2n+1)=3*(n+2)+10 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"2%2A%282%2An%2B1%29=highlight_red%28+3%2A%28n%2B2%29%2B10+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-3%2A%28n%2B2%29+%29\"$ , $\"highlight_green%28+-10+%29\"$
It becomes $\"2%2A%282%2An%2B1%29-highlight_green%28+3%2A%28n%2B2%29+%29-highlight_green%28+10+%29=0\"$ .
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Look at $\"highlight_red%28+2%2A%282%2An%2B1%29+%29-3%2A%28n%2B2%29-10=0\"$ .
Expanded term $\"2\"$ by using associative property on $\"%282%2An%2B1%29\"$
It becomes $\"highlight_green%28+2%2A2%2An+%29%2Bhighlight_green%28+2%2A1+%29-3%2A%28n%2B2%29-10=0\"$ .
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Look at $\"highlight_red%28+2+%29%2Ahighlight_red%28+2+%29%2An%2B2%2A1-3%2A%28n%2B2%29-10=0\"$ .
Multiplied numerator integers
It becomes $\"highlight_green%28+4+%29%2An%2B2%2A1-3%2A%28n%2B2%29-10=0\"$ .
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Look at $\"4%2An%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+1+%29-3%2A%28n%2B2%29-10=0\"$ .
Multiplied numerator integers
It becomes $\"4%2An%2Bhighlight_green%28+2+%29-3%2A%28n%2B2%29-10=0\"$ .
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Look at $\"4%2An%2Bhighlight_red%28+2+%29-3%2A%28n%2B2%29-highlight_red%28+10+%29=0\"$ .
Added fractions or integers together
It becomes $\"4%2An%2Bhighlight_green%28+-8+%29-3%2A%28n%2B2%29=0\"$ .
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Look at $\"4%2An%2Bhighlight_red%28+-8+%29-3%2A%28n%2B2%29=0\"$ .
Moved $\"-8\"$ to the right of expression
It becomes $\"4%2An-3%2A%28n%2B2%29%2Bhighlight_green%28+-8+%29=0\"$ .
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Look at $\"4%2An-3%2A%28n%2B2%29%2Bhighlight_red%28+-8+%29=0\"$ .
Removed extra sign in front of $\"-8\"$
It becomes $\"4%2An-3%2A%28n%2B2%29-highlight_green%28+8+%29=0\"$ .
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Look at $\"4%2An-highlight_red%28+3%2A%28n%2B2%29+%29-8=0\"$ .
Expanded term $\"-3\"$ by using associative property on $\"%28n%2B2%29\"$
It becomes $\"4%2An-highlight_green%28+3%2An+%29-highlight_green%28+3%2A2+%29-8=0\"$ .
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Look at $\"4%2An-3%2An-highlight_red%28+3+%29%2Ahighlight_red%28+2+%29-8=0\"$ .
Multiplied numerator integers
It becomes $\"4%2An-3%2An-highlight_green%28+6+%29-8=0\"$ .
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Look at $\"4%2An-3%2An-highlight_red%28+6+%29-highlight_red%28+8+%29=0\"$ .
Added fractions or integers together
It becomes $\"4%2An-3%2An%2Bhighlight_green%28+-14+%29=0\"$ .
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Look at $\"4%2An-3%2An%2Bhighlight_red%28+-14+%29=0\"$ .
Removed extra sign in front of $\"-14\"$
It becomes $\"4%2An-3%2An-highlight_green%28+14+%29=0\"$ .
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Look at $\"highlight_red%28+4%2An+%29-highlight_red%28+3%2An+%29-14=0\"$ .
Eliminated similar terms $\"highlight_red%28+4%2An+%29\"$ , $\"highlight_red%28+-3%2An+%29\"$ replacing them with $\"highlight_green%28+%284-3%29%2An+%29\"$
It becomes $\"highlight_green%28+%284-3%29%2An+%29-14=0\"$ .
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Look at $\"highlight_red%28+%284-3%29+%29%2An-14=0\"$ .
Remove extraneous '1' from product $\"highlight_red%28+%284-3%29+%29\"$
It becomes $\"n-14=0\"$ .
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Look at $\"highlight_red%28+n-14+%29=0\"$ .
Solved linear equation $\"highlight_red%28+n-14=0+%29\"$ equivalent to n-14 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: n=14.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "n=14, then n+1=15 and n+2=16\r
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\n" ); document.write( "\n" ); document.write( "Check original equation $\"2%282n%2B1%29=3%28n%2B2%29%2B10\"$ or $\"2%2814%2B15%29=3%2A16%2B10\"$ such that $\"58=58\"$ which is a true statement.\r
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\n" ); document.write( "\n" ); document.write( "Step 8. ANSWER: The three consecutive integers are 14, 15, and 16.\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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\n" ); document.write( "\n" ); document.write( "I hope the above steps were helpful.\r
\n" ); document.write( "
\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
\n" ); document.write( "
\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 \n" ); document.write( "

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