document.write( "Question 34457: On the first day of school, the percentage of boys in a particular class is 60%. During the school year, six girls move away, and are replaced in the class by six boys; this makes the class roster 75% boys. Find the number of boys and girls in the class on the first day of school. \n" ); document.write( "

Algebra.Com's Answer #20736 by lyra(94) $\"\"$ $\"About$

You can put this solution on YOUR website!
Alright, so we want to write the \"words\" as \"math\". \r
\n" ); document.write( "\n" ); document.write( " $\".6x%2Bg=x\"$
\n" ); document.write( " $\".75x%2Bg=x\"$
\n" ); document.write( " $\".6x%2B%28g-6%29=.75x%2Bg\"$
\n" ); document.write( " $\".6x-.6x%2B%28g-6%29=.75x-.6x%2Bg\"$
\n" ); document.write( " $\"g-6=.15x%2Bg\"$
\n" ); document.write( " $\"100%28g-6%29=100%28.15x%2Bg%29\"$
\n" ); document.write( " $\"100g-600=15x%2B100g\"$
\n" ); document.write( " $\"100g-600-100g=15x%2B100g-100g\"$
\n" ); document.write( " $\"-600=15x\"$
\n" ); document.write( " $\"-600%2F15=15x%2F15\"$
\n" ); document.write( " $\"-40=x\"$
\n" ); document.write( "See also,
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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: x=-40.
Graphical form: Equation $\".6x%2B%28g-6%29=.75x%2Bg\"$ was fully solved.
Text form: .6x+(g-6)=.75x+g simplifies to 0=0
Cartoon (animation) form: $\"simplify_cartoon%28+.6x%2B%28g-6%29=.75x%2Bg+%29\"$
For tutors: simplify_cartoon( .6x+(g-6)=.75x+g )
If you have a website, here's a link to this solution.

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DETAILED EXPLANATION

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Look at $\".6%2Ax%2Bhighlight_red%28+%28g-6%29+%29=.75x%2Bg\"$ .
Remove unneeded parentheses around terms $\"highlight_red%28+g+%29\"$ , $\"highlight_red%28+-6+%29\"$
It becomes $\".6%2Ax%2Bhighlight_green%28+g+%29-highlight_green%28+6+%29=.75x%2Bg\"$ .
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Look at $\".6%2Ax%2Bg-6=highlight_red%28+.75%2Ax%2Bg+%29\"$ .
Moved these terms to the left $\"highlight_green%28+-.75%2Ax+%29\"$ , $\"highlight_green%28+-g+%29\"$
It becomes $\".6%2Ax%2Bg-6-highlight_green%28+.75%2Ax+%29-highlight_green%28+g+%29=0\"$ .
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Look at $\".6%2Ax%2Bg-highlight_red%28+6+%29-.75%2Ax-g=0\"$ .
Moved $\"-6\"$ to the right of expression
It becomes $\".6%2Ax%2Bg-.75%2Ax-g-highlight_green%28+6+%29=0\"$ .
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Look at $\"highlight_red%28+.6%2Ax+%29%2Bg-highlight_red%28+.75%2Ax+%29-g-6=0\"$ .
Eliminated similar terms $\"highlight_red%28+.6%2Ax+%29\"$ , $\"highlight_red%28+-.75%2Ax+%29\"$ replacing them with $\"highlight_green%28+%28.6-.75%29%2Ax+%29\"$
It becomes $\"highlight_green%28+%28.6-.75%29%2Ax+%29%2Bg-g-6=0\"$ .
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Look at $\"%28.6-.75%29%2Ax%2Bhighlight_red%28+g+%29-highlight_red%28+g+%29-6=0\"$ .
Eliminated similar terms $\"highlight_red%28+g+%29\"$ , $\"highlight_red%28+-g+%29\"$ replacing them with $\"highlight_green%28+%281-1%29%2Ag+%29\"$
It becomes $\"%28.6-.75%29%2Ax%2Bhighlight_green%28+%281-1%29%2Ag+%29-6=0\"$ .
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Look at $\"%28highlight_red%28+.6+%29-highlight_red%28+.75+%29%29%2Ax%2B%281-1%29%2Ag-6=0\"$ .
Replace constants in expression: $\"highlight_red%28+.6+%29\"$ , $\"highlight_red%28+-.75+%29\"$ with $\"highlight_green%28+-0.15+%29\"$
It becomes $\"%28highlight_green%28+-0.15+%29%29%2Ax%2B%281-1%29%2Ag-6=0\"$ .
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Look at $\"%28-0.15%29%2Ax%2Bhighlight_red%28+%281-1%29%2Ag+%29-6=0\"$ .
Since $\"highlight_red%28+%281-1%29%2Ag+%29\"$ has zero as a factor, it should be replaced with a zero
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Look at $\"%28-0.15%29%2Ax%2B0-6=0\"$ .
Added fractions or integers together
It becomes $\"%28-0.15%29%2Ax%2B0-6=0\"$ .
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Look at $\"%28-0.15%29%2Ax%2Bhighlight_red%28+0+%29-6=0\"$ .
Remove extraneous zero $\"highlight_red%28+0+%29\"$
It becomes $\"%28-0.15%29%2Ax-6=0\"$ .
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Look at $\"%28highlight_red%28+-0.15+%29%29%2Ax-6=0\"$ .
Removed extra sign in front of $\"-0.15\"$
It becomes $\"%28-highlight_green%28+0.15+%29%29%2Ax-6=0\"$ .
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Look at $\"highlight_red%28+%28-highlight_red%28+0.15+%29%29%2Ax+%29-6=0\"$ .
Remove unneeded parentheses around factor $\"highlight_red%28+0.15+%29\"$
It becomes $\"-highlight_green%28+0.15+%29%2Ax-6=0\"$ .
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Look at $\"highlight_red%28+-0.15%2Ax-6+%29=0\"$ .
Solved linear equation $\"highlight_red%28+-0.15%2Ax-6=0+%29\"$ equivalent to -0.15*x-6 =0
It becomes $\"highlight_green%28+0+%29=0\"$ .
Result: $\"0=0\"$
\n" ); document.write( "This is an equation! Solutions: x=-40.

Universal Simplifier and Solver

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Done!

\n" ); document.write( "\n" ); document.write( "Since there can't be a negative amount of people, we remove the negative sign getting:
\n" ); document.write( " $\"x=40\"$
\n" ); document.write( "Now we plug this into the original equation:
\n" ); document.write( " $\".6%2840%29%2Bg=40\"$
\n" ); document.write( " $\"24%2Bg=40\"$ So there are 24 boys in the class.
\n" ); document.write( " $\"24-24%2Bg=40-24\"$
\n" ); document.write( " $\"g=16\"$ There are 16 girls in the class.
\n" ); document.write( "So the answer is that on the first day of class there were 16 girls and 24 boys.\r
\n" ); document.write( "\n" ); document.write( "We can check that our answer works:
\n" ); document.write( " $\".6%2A40=24\"$ That works
\n" ); document.write( " $\".4%2A40=16\"$ That works
\n" ); document.write( " $\"16-6=10\"$
\n" ); document.write( " $\"24%2B6=30\"$
\n" ); document.write( " $\".75%2A40=30\"$ That works
\n" ); document.write( " $\".25%2A40=10\"$ That works
\n" ); document.write( "Yep, everything checks, we have the right answer.\r
\n" ); document.write( "\n" ); document.write( "Hope this helps,
\n" ); document.write( "lyra
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