document.write( "Question 215647: finding three consecutive integers such that the sum of the first, twice the second, and three times the third is 62 \n" ); document.write( "

Algebra.Com's Answer #162973 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
Finding three consecutive integers such that the sum of the first, twice the second, and three times the third is 62 \r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let n be one integer, \r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let n+1 be the second consecutive number and 2(n+1) is twice the second number \r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let n+2 is the third consecutive number and 3(n+2) is three times the third\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Then the sum is n+2(n+1)+3(n+2)=62 as given by the problem statement. The following steps will solve this equation.\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=9.
Graphical form: Equation $\"n%2B2%2A%28n%2B1%29%2B3%2A%28n%2B2%29=62\"$ was fully solved.
Text form: n+2*(n+1)+3*(n+2)=62 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+n%2B2%2A%28n%2B1%29%2B3%2A%28n%2B2%29=62+%29\"$
For tutors: simplify_cartoon( n+2*(n+1)+3*(n+2)=62 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"n%2B2%2A%28n%2B1%29%2B3%2A%28n%2B2%29=highlight_red%28+62+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-62+%29\"$
It becomes $\"n%2B2%2A%28n%2B1%29%2B3%2A%28n%2B2%29-highlight_green%28+62+%29=0\"$ .
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Look at $\"n%2Bhighlight_red%28+2%2A%28n%2B1%29+%29%2B3%2A%28n%2B2%29-62=0\"$ .
Expanded term $\"2\"$ by using associative property on $\"%28n%2B1%29\"$
It becomes $\"n%2Bhighlight_green%28+2%2An+%29%2Bhighlight_green%28+2%2A1+%29%2B3%2A%28n%2B2%29-62=0\"$ .
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Look at $\"n%2B2%2An%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+1+%29%2B3%2A%28n%2B2%29-62=0\"$ .
Multiplied numerator integers
It becomes $\"n%2B2%2An%2Bhighlight_green%28+2+%29%2B3%2A%28n%2B2%29-62=0\"$ .
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Look at $\"n%2B2%2An%2Bhighlight_red%28+2+%29%2B3%2A%28n%2B2%29-highlight_red%28+62+%29=0\"$ .
Added fractions or integers together
It becomes $\"n%2B2%2An%2Bhighlight_green%28+-60+%29%2B3%2A%28n%2B2%29=0\"$ .
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Look at $\"n%2B2%2An%2Bhighlight_red%28+-60+%29%2B3%2A%28n%2B2%29=0\"$ .
Moved $\"-60\"$ to the right of expression
It becomes $\"n%2B2%2An%2B3%2A%28n%2B2%29%2Bhighlight_green%28+-60+%29=0\"$ .
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Look at $\"n%2B2%2An%2B3%2A%28n%2B2%29%2Bhighlight_red%28+-60+%29=0\"$ .
Removed extra sign in front of $\"-60\"$
It becomes $\"n%2B2%2An%2B3%2A%28n%2B2%29-highlight_green%28+60+%29=0\"$ .
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Look at $\"highlight_red%28+n+%29%2Bhighlight_red%28+2%2An+%29%2B3%2A%28n%2B2%29-60=0\"$ .
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 $\"highlight_green%28+%281%2B2%29%2An+%29%2B3%2A%28n%2B2%29-60=0\"$ .
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Look at $\"%28highlight_red%28+1+%29%2Bhighlight_red%28+2+%29%29%2An%2B3%2A%28n%2B2%29-60=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+3+%29%29%2An%2B3%2A%28n%2B2%29-60=0\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+3+%29%29%2An+%29%2B3%2A%28n%2B2%29-60=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+3+%29\"$
It becomes $\"highlight_green%28+3+%29%2An%2B3%2A%28n%2B2%29-60=0\"$ .
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Look at $\"3%2An%2Bhighlight_red%28+3%2A%28n%2B2%29+%29-60=0\"$ .
Expanded term $\"3\"$ by using associative property on $\"%28n%2B2%29\"$
It becomes $\"3%2An%2Bhighlight_green%28+3%2An+%29%2Bhighlight_green%28+3%2A2+%29-60=0\"$ .
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Look at $\"3%2An%2B3%2An%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+2+%29-60=0\"$ .
Multiplied numerator integers
It becomes $\"3%2An%2B3%2An%2Bhighlight_green%28+6+%29-60=0\"$ .
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Look at $\"3%2An%2B3%2An%2Bhighlight_red%28+6+%29-highlight_red%28+60+%29=0\"$ .
Added fractions or integers together
It becomes $\"3%2An%2B3%2An%2Bhighlight_green%28+-54+%29=0\"$ .
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Look at $\"3%2An%2B3%2An%2Bhighlight_red%28+-54+%29=0\"$ .
Removed extra sign in front of $\"-54\"$
It becomes $\"3%2An%2B3%2An-highlight_green%28+54+%29=0\"$ .
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Look at $\"highlight_red%28+3%2An+%29%2Bhighlight_red%28+3%2An+%29-54=0\"$ .
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 $\"highlight_green%28+%283%2B3%29%2An+%29-54=0\"$ .
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Look at $\"%28highlight_red%28+3+%29%2Bhighlight_red%28+3+%29%29%2An-54=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+6+%29%29%2An-54=0\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+6+%29%29%2An+%29-54=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+6+%29\"$
It becomes $\"highlight_green%28+6+%29%2An-54=0\"$ .
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Look at $\"highlight_red%28+6%2An-54+%29=0\"$ .
Solved linear equation $\"highlight_red%28+6%2An-54=0+%29\"$ equivalent to 6*n-54 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: n=9.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "With n= 9, then n+1= 10 , and n+2=11\r
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\n" ); document.write( "\n" ); document.write( "Check sum..9+2*10+3*11=9+20+33=622...which is a true statement.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. ANSWER: The numbers are 9, 10, and 11. \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 on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or 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
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