Question 1047264
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Now that you have finally stated the problem correctly, we can find a correct solution.


The fact that Matthew took two fewer cookies for himself means that if he had started with two more cookies, he could have split them evenly between himself and his friends.  Let *[tex \Large n] represent the number of friends and *[tex \Large x] represent the number of cookies each receives, we can state:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (n\ +\ 1)x\ =\ 35].


Since both *[tex \Large n] and *[tex \Large x] must be integers (Matthew doesn't have fractional parts of friends and the problem implies whole numbers of cookies were distributed), and the prime factorization of 35 is 5 times 7, the number of friends must be either 4 or 6 and the number of cookies given to each of the friends must be either 7 or 5.


If there are 4 friends, and each gets 7 cookies, that makes 28 cookies distributed to friends, plus the two fewer cookies (5) that Matt keeps, makes 33.


If there are 6 friends, and each gets 5 cookies, that makes 30 cookies distributed to friends, plus the two fewer cookies (3) that Matt keeps, makes 33.


Hence, Matt either has 4 friends or 6 friends.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

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