Grandma baked 96 cookies and gave them to her grandchildren. one of the grandchildren, cindy, received 5 fewer cookies than she would have received had all of the cookies been evenly divided among the h grandchildren.
how many cookies did cindy receive?
write your answer as an expression.

If the cookies had been divided equally between the h grandchildren then each grandchild would receive 96/h  cookies.
So Cindy  received (96/h) - 5   cookies

Does not say how many grandchildren. Say n, integer. So, all received some cookies, x, except Cindy, who received 5 less than the even number:

even number= 96/n, Cindy gets 96/n-5, the rest receive the rest of the cookies:

96 - (96/n-5) = 96*(1-1/n) + 5 = 96*(n-1)/n + 5.

Then each of them (n-1) receive the previous number divided by (n-1) -Cindy is not there:

each of the other grandchildren receives:

96/n + 5/(n-1), and Cindy receives 96/n-5, it just needs to be positive.

So any number 'n' which divides 96 and 'n-1' divides 5 works.

Indeed ONLY n=6, makes 5/(6-1) possible.

So there are 6 grandchildren:

5 receive 17 cookies, and Cindy gets 11.

If it were evenly distributed, all would have got 96/6 = 16 cookies.

Now 5 get one more cookie, and Cindy 5 less.

WOW. Very nice problem!! Gonna share it :)

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