A breakfast-food company have a contest. Each breakfast-food carton has a number in it.  A prize of $1000 is awarded to anyone who can collect numbers with a sum of 100, made from any number of cards.  The following numbers are used.               3            12          15          18          27          33          45          51          66          75          84          90 Jim buys enough cartons and trades with friends so he has one of each number. a)      Does Jim have a winning combination using each card only once?  Explain why or why not.  If the company is going to add one more number to the list and so the contest has many more winners, what number would you suggest and why?

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