document.write( "Question 223809: if five times the smaller of two consecutive integers is added to three times the, the result is 59. Find bothe numbers \n" ); document.write( "

Algebra.Com's Answer #167278 by drj(1380) $\"\"$ $\"About$

You can put this solution on YOUR website!
If five times the smaller of two consecutive integers is added to three times the larger integer, the result is 59. Find both numbers.\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 next consecutive integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 3. Let 5n be five times the smaller integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 4. Let 3(n+1) be three times the larger integer.\r
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\n" ); document.write( "\n" ); document.write( "Step 5. Then 5n+3(n+1)=59 since five times the smaller of two consecutive integers is added to three times the larger integer, the result is 59.\r
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\n" ); document.write( "\n" ); document.write( "Step 6. Solving the equation in Step 5 leads to 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=7.
Graphical form: Equation $\"5n%2B3%2A%28n%2B1%29=59\"$ was fully solved.
Text form: 5n+3*(n+1)=59 simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+5n%2B3%2A%28n%2B1%29=59+%29\"$
For tutors: simplify_cartoon( 5n+3*(n+1)=59 )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\"5%2An%2B3%2A%28n%2B1%29=highlight_red%28+59+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-59+%29\"$
It becomes $\"5%2An%2B3%2A%28n%2B1%29-highlight_green%28+59+%29=0\"$ .
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Look at $\"5%2An%2Bhighlight_red%28+3%2A%28n%2B1%29+%29-59=0\"$ .
Expanded term $\"3\"$ by using associative property on $\"%28n%2B1%29\"$
It becomes $\"5%2An%2Bhighlight_green%28+3%2An+%29%2Bhighlight_green%28+3%2A1+%29-59=0\"$ .
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Look at $\"5%2An%2B3%2An%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+1+%29-59=0\"$ .
Multiplied numerator integers
It becomes $\"5%2An%2B3%2An%2Bhighlight_green%28+3+%29-59=0\"$ .
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Look at $\"5%2An%2B3%2An%2Bhighlight_red%28+3+%29-highlight_red%28+59+%29=0\"$ .
Added fractions or integers together
It becomes $\"5%2An%2B3%2An%2Bhighlight_green%28+-56+%29=0\"$ .
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Look at $\"5%2An%2B3%2An%2Bhighlight_red%28+-56+%29=0\"$ .
Removed extra sign in front of $\"-56\"$
It becomes $\"5%2An%2B3%2An-highlight_green%28+56+%29=0\"$ .
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Look at $\"highlight_red%28+5%2An+%29%2Bhighlight_red%28+3%2An+%29-56=0\"$ .
Eliminated similar terms $\"highlight_red%28+5%2An+%29\"$ , $\"highlight_red%28+3%2An+%29\"$ replacing them with $\"highlight_green%28+%285%2B3%29%2An+%29\"$
It becomes $\"highlight_green%28+%285%2B3%29%2An+%29-56=0\"$ .
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Look at $\"%28highlight_red%28+5+%29%2Bhighlight_red%28+3+%29%29%2An-56=0\"$ .
Added fractions or integers together
It becomes $\"%28highlight_green%28+8+%29%29%2An-56=0\"$ .
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Look at $\"highlight_red%28+%28highlight_red%28+8+%29%29%2An+%29-56=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+8+%29\"$
It becomes $\"highlight_green%28+8+%29%2An-56=0\"$ .
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Look at $\"highlight_red%28+8%2An-56+%29=0\"$ .
Solved linear equation $\"highlight_red%28+8%2An-56=0+%29\"$ equivalent to 8*n-56 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: n=7.

Universal Simplifier and Solver

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Done!

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\n" ); document.write( "\n" ); document.write( "With n=7, then n+1=8. Check sum... 5*7+3*8=35+24=59 which is a true statement.\r
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\n" ); document.write( "\n" ); document.write( "Step 7. The consecutive integers are 7 and 8.\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 \n" ); document.write( "

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