document.write( "Question 1103857: The officers of a math club will pay equal contributions to buy a cake worth $480 for their moderator. If there were two more officers, their contribution will be reduced by $12 each. How many officers are there? \n" ); document.write( "

Algebra.Com's Answer #718559 by Fombitz(32388) $\"\"$ $\"About$

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Let there be $\"N\"$ officers.
\n" ); document.write( "So for each officer it would cost,
\n" ); document.write( " $\"480%2FN\"$
\n" ); document.write( "Increasing the number by two, the cost would be,
\n" ); document.write( " $\"480%2F%28N%2B2%29\"$
\n" ); document.write( "So the difference is,
\n" ); document.write( " $\"480%2FN-480%2F%28N%2B2%29=12\"$
\n" ); document.write( " $\"40%2FN-40%2F%28N%2B2%29=1\"$
\n" ); document.write( " $\"40%28N%2B2%29-40N=N%28N%2B2%29\"$
\n" ); document.write( " $\"40N%2B80-40N=N%5E2%2B2N\"$
\n" ); document.write( " $\"N%5E2%2B2N-80=0\"$
\n" ); document.write( " $\"%28N%2B10%29%28N-8%29=0\"$
\n" ); document.write( "Only positive solutions for N make sense here.
\n" ); document.write( " $\"N-8=0\"$
\n" ); document.write( " $\"N=8\"$
\n" ); document.write( " \n" ); document.write( "

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