SOLUTION: 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 receiv

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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?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= number of M&M snacks the wizard had received
6x= 6 times the number of M&M snacks the wizard had received
x-5= five less than the number of M&M snacks the wizard received
x%5E2= the square of the number of M&M snacks the wizard received

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