document.write( "Question 784773: one Halloween evening a wizard and a witch countes the number of m&m snacks they had eacch received as a result their trick or treating. The witch simply said that she had received 7 of them. The wizard, being a math genius, noticed that if he divided 6times the number of m&m snacka that he received by five less than the number he received, he woukd have the square of the number of m&m snacks that he had received. Who had more m&ms, the witch or the wizard? \n" ); document.write( "

Algebra.Com's Answer #477302 by KMST(5328) $\"\"$ $\"About$

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$\"x\"$ = number of M&M snacks the wizard had received
\n" ); document.write( " $\"6x\"$ = 6 times the number of M&M snacks the wizard had received
\n" ); document.write( " $\"x-5\"$ = five less than the number of M&M snacks the wizard received
\n" ); document.write( " $\"x%5E2\"$ = the square of the number of M&M snacks the wizard received
\n" ); document.write( "
\n" ); document.write( "What the wizard says in words, translates as
\n" ); document.write( " $\"6x%2F%28x-5%29=x%5E2\"$
\n" ); document.write( "To solve that equation, I would first multiply both sides of the equal sign times $\"%28x-5%29\"$ to eliminate the denominator, and get
\n" ); document.write( " $\"6x=x%5E2%28x-5%29\"$
\n" ); document.write( "Then, it can be transformed and factored:
\n" ); document.write( " $\"6x=x%5E2%28x-5%29\"$ --> $\"6x=x%5E3-5x%5E2\"$ --> $\"x%5E3-5x%5E2-6x=0\"$ --> $\"x%28x%5E2-5x-6%29=0\"$ --> $\"x%28x-6%29%28x%2B1%29=0\"$
\n" ); document.write( "THe solutions to that equation are:
\n" ); document.write( " $\"x=-1\"$ (which qould not make sense,
\n" ); document.write( " $\"x=0\"$ (maybe the wizard did not get any M&M), and
\n" ); document.write( " $\"x=6\"$ .\r
\n" ); document.write( "\n" ); document.write( "The wizard may have received 6 M&M's or none at all, but the witch, who got 7, had more M&M's. \n" ); document.write( "

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