A third-grade class is told to send a cookie to every single one of their classmates. When the boxes arrive, the class ends up with 306 cookies. How many pupils are in the class
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According to the question, each of the classmates is supposed to send a cookie to every other classmate, and we have 306 cookies in the end.
Suppose we take each classmate as ‘a’
Now ‘a’ has to send a cookie to every other classmate excluding himself, which means he has to send it to ‘a-1’
Total number of cookies is 306, now the equation becomes –
a(a-1) = 306, Again,
a2 –a = 306
a2-a -306 =0
a2+17a-18a-306 = 0
a(a+17) -18(a+17) =0
(a+17)(a-18) = 0
A= -17, or a= 18
The positive figure a = 18 is the correct answer, There were 18 pupils in the class.
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