document.write( "Question 215166: If 3 times the smaller of two consecutive integers is added to 4 times the larger, the result is 102, Find the larger integer. \n" ); document.write( "

Algebra.Com's Answer #162586 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
If 3 times the smaller of two consecutive integers is added to 4 times the larger, the result is 102, Find the larger integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 1. Let n be one integer and let n+1 be the next consecutive integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 2. Let 4(n+1) is 4 times the larger integer\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let 3n is 3 times the smaller integer\r
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\n" ); document.write( "\n" ); document.write( "Step 4. 3n+4(n+1)=102 3 times the smaller of two consecutive integers is added to 4 times the larger, the result is 102\r
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\n" ); document.write( "\n" ); document.write( "Step 5. The following steps 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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This is an equation! Solutions: n=14.
Graphical form: Equation $\"3n%2B4%2A%28n%2B1%29=102\"$ was fully solved.
Text form: 3n+4*(n+1)=102 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+3n%2B4%2A%28n%2B1%29=102+%29\"$
For tutors: simplify_cartoon( 3n+4*(n+1)=102 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"3%2An%2B4%2A%28n%2B1%29=highlight_red%28+102+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-102+%29\"$
It becomes $\"3%2An%2B4%2A%28n%2B1%29-highlight_green%28+102+%29=0\"$ .
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Look at $\"3%2An%2Bhighlight_red%28+4%2A%28n%2B1%29+%29-102=0\"$ .
Expanded term $\"4\"$ by using associative property on $\"%28n%2B1%29\"$
It becomes $\"3%2An%2Bhighlight_green%28+4%2An+%29%2Bhighlight_green%28+4%2A1+%29-102=0\"$ .
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Look at $\"3%2An%2B4%2An%2Bhighlight_red%28+4+%29%2Ahighlight_red%28+1+%29-102=0\"$ .
Multiplied numerator integers
It becomes $\"3%2An%2B4%2An%2Bhighlight_green%28+4+%29-102=0\"$ .
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Look at $\"3%2An%2B4%2An%2Bhighlight_red%28+4+%29-highlight_red%28+102+%29=0\"$ .
Added fractions or integers together
It becomes $\"3%2An%2B4%2An%2Bhighlight_green%28+-98+%29=0\"$ .
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Look at $\"3%2An%2B4%2An%2Bhighlight_red%28+-98+%29=0\"$ .
Removed extra sign in front of $\"-98\"$
It becomes $\"3%2An%2B4%2An-highlight_green%28+98+%29=0\"$ .
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Look at $\"highlight_red%28+3%2An+%29%2Bhighlight_red%28+4%2An+%29-98=0\"$ .
Eliminated similar terms $\"highlight_red%28+3%2An+%29\"$ , $\"highlight_red%28+4%2An+%29\"$ replacing them with $\"highlight_green%28+%283%2B4%29%2An+%29\"$
It becomes $\"highlight_green%28+%283%2B4%29%2An+%29-98=0\"$ .
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Look at $\"%28highlight_red%28+3+%29%2Bhighlight_red%28+4+%29%29%2An-98=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+7+%29%29%2An-98=0\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+7+%29%29%2An+%29-98=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+7+%29\"$
It becomes $\"highlight_green%28+7+%29%2An-98=0\"$ .
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Look at $\"highlight_red%28+7%2An-98+%29=0\"$ .
Solved linear equation $\"highlight_red%28+7%2An-98=0+%29\"$ equivalent to 7*n-98 =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( "With n=14 , then n+1=15\r
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\n" ); document.write( "\n" ); document.write( "Check 3*14+4*15=102 or 102=102 which is a true statement\r
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\n" ); document.write( "\n" ); document.write( "Step 6. The integers are 14 and 15 where 15 is the larger 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 on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.\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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