Eleanor is making chocolate chip cookies for her friends. If she divides the cookies equally among 11 of her friends, she'll have 4 cookies left over. If she divides the cookies equally among 7 of her friends, she'll have 1 cookie left over. Assuming that Eleanor made fewer than 100 cookies, what is the sum of the possible numbers of cookies that she could have made?
...The only number I could find was 15, but 15 isn't the correct answer. Please help!
+129840 Let N be the number of cookies
And we have that
N = 11m + 4
N = 7n + 1 subtracting the second equation form the first, we have
11m - 7n = -3 → 11m = 7n - 3
And the only possible values for {m,n} are {1, 2} or (8, 13}
Thus N could be either 15 or 92
And their sum = 106
+37091 Phil is correct (as usual) ...I do not know how I came up with 59 while I was on my bike ride doing this in my head this morning.....
HOWEVER 92 + 15 equals 107 NOT 106 as Phil added.
