document.write( "Question 1012100: At a school camp 5 people could be accommodated per room but 3 people leftover.if each room had 6 people, 2 rooms would be left over. How many students attended the camp? \n" ); document.write( "
Algebra.Com's Answer #627957 by ValorousDawn(53)\"\" \"About 
You can put this solution on YOUR website!
Lets say there are an x number of rooms.
\n" ); document.write( "5x+3=6(x-2)
\n" ); document.write( "The two sides of the equation represent the number of people. If each room can fit 5 people, and there are an x number of rooms, there are 5x people, but with 3 leftover, so we add 3. The right side has x-2 in parenthesis, because there are 2 fewer rooms, but we change the 5 to a 6, as there are now 6 people a room.
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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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  • This is an equation! Solutions: x=15.
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  • Graphical form: Equation \"5x%2B3=6%2A%28x-2%29\" was fully solved.
  • Text form: 5x+3=6*(x-2) simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+5x%2B3=6%2A%28x-2%29+%29\"
    For tutors: simplify_cartoon( 5x+3=6*(x-2) )
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  • 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%2Ax%2B3=highlight_red%28+6%2A%28x-2%29+%29\".
Moved these terms to the left \"highlight_green%28+-6%2A%28x-2%29+%29\"
It becomes \"5%2Ax%2B3-highlight_green%28+6%2A%28x-2%29+%29=0\".
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Look at \"5%2Ax%2Bhighlight_red%28+3+%29-6%2A%28x-2%29=0\".
Moved \"3\" to the right of expression
It becomes \"5%2Ax-6%2A%28x-2%29%2Bhighlight_green%28+3+%29=0\".
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Look at \"5%2Ax-highlight_red%28+6%2A%28x-2%29+%29%2B3=0\".
Expanded term \"-6\" by using associative property on \"%28x-2%29\"
It becomes \"5%2Ax-highlight_green%28+6%2Ax+%29%2Bhighlight_green%28+6%2A2+%29%2B3=0\".
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Look at \"5%2Ax-6%2Ax%2Bhighlight_red%28+6+%29%2Ahighlight_red%28+2+%29%2B3=0\".
Multiplied numerator integers
It becomes \"5%2Ax-6%2Ax%2Bhighlight_green%28+12+%29%2B3=0\".
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Look at \"5%2Ax-6%2Ax%2Bhighlight_red%28+12+%29%2Bhighlight_red%28+3+%29=0\".
Added fractions or integers together
It becomes \"5%2Ax-6%2Ax%2Bhighlight_green%28+15+%29=0\".
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Look at \"highlight_red%28+5%2Ax+%29-highlight_red%28+6%2Ax+%29%2B15=0\".
Eliminated similar terms \"highlight_red%28+5%2Ax+%29\",\"highlight_red%28+-6%2Ax+%29\" replacing them with \"highlight_green%28+%285-6%29%2Ax+%29\"
It becomes \"highlight_green%28+%285-6%29%2Ax+%29%2B15=0\".
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Look at \"%28highlight_red%28+5+%29-highlight_red%28+6+%29%29%2Ax%2B15=0\".
Added fractions or integers together
It becomes \"%28highlight_green%28+-1+%29%29%2Ax%2B15=0\".
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Look at \"%28highlight_red%28+-1+%29%29%2Ax%2B15=0\".
Removed extra sign in front of \"-1\"
It becomes \"%28-highlight_green%28+1+%29%29%2Ax%2B15=0\".
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Look at \"highlight_red%28+%28-highlight_red%28+1+%29%29%2Ax+%29%2B15=0\".
Remove unneeded parentheses around factor \"highlight_red%28+1+%29\"
It becomes \"-highlight_green%28+1+%29%2Ax%2B15=0\".
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Look at \"-highlight_red%28+1+%29%2Ax%2B15=0\".
Remove extraneous '1' from product \"highlight_red%28+1+%29\"
It becomes \"-x%2B15=0\".
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Look at \"highlight_red%28+-x%2B15+%29=0\".
Solved linear equation \"highlight_red%28+-x%2B15=0+%29\" equivalent to -x+15 =0
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
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Universal Simplifier and Solver

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Done!

\n" ); document.write( "\n" ); document.write( "With 15 people per room, you can plug it into either equation to find the number of people.
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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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  • Graphical form: \"5%2A%2815%29%2B3\" simplifies to \"78\"
  • Text form: 5*(15)+3 simplifies to 78
  • Cartoon (animation) form: \"simplify_cartoon%28+5%2A%2815%29%2B3+%29\"
    For tutors: simplify_cartoon( 5*(15)+3 )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at \"highlight_red%28+5%2A%28highlight_red%28+15+%29%29+%29%2B3\".
Remove unneeded parentheses around factor \"highlight_red%28+15+%29\"
It becomes \"5%2Ahighlight_green%28+15+%29%2B3\".
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Look at \"highlight_red%28+5+%29%2Ahighlight_red%28+15+%29%2B3\".
Multiplied numerator integers
It becomes \"highlight_green%28+75+%29%2B3\".
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Look at \"highlight_red%28+75+%29%2Bhighlight_red%28+3+%29\".
Added fractions or integers together
It becomes \"highlight_green%28+78+%29\".
Result: \"78\"
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Universal Simplifier and Solver

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Done!

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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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  • Graphical form: \"6%2A%2815-2%29\" simplifies to \"78\"
  • Text form: 6*(15-2) simplifies to 78
  • Cartoon (animation) form: \"simplify_cartoon%28+6%2A%2815-2%29+%29\"
    For tutors: simplify_cartoon( 6*(15-2) )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at \"6%2A%28highlight_red%28+15+%29-highlight_red%28+2+%29%29\".
Added fractions or integers together
It becomes \"6%2A%28highlight_green%28+13+%29%29\".
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Look at \"highlight_red%28+6%2A%28highlight_red%28+13+%29%29+%29\".
Remove unneeded parentheses around factor \"highlight_red%28+13+%29\"
It becomes \"6%2Ahighlight_green%28+13+%29\".
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Look at \"highlight_red%28+6+%29%2Ahighlight_red%28+13+%29\".
Multiplied numerator integers
It becomes \"highlight_green%28+78+%29\".
Result: \"78\"
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Universal Simplifier and Solver

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Done!

\n" ); document.write( "\n" ); document.write( "Therefore there are 78 people at the camp. \n" ); document.write( "
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