In a class of 25 students, 2 students did not borrow any books from the library, 10 students each borrowed 1 book, 8 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed ? Choose the correct choice from the following choices:
A) 8
B) 10
C) 12
D) 13
E) 15
The average number of books per student was 2means that total of   2*25= 
<gadget id="calculator">  2*25</gadget>
<output>50</output>
50 books were borrowed;   2+10+8= 
<gadget id="calculator">2+10+8</gadget>
<output>20</output>
20 students borrowed total of  2*0+10*1+8*2= 
<gadget id="calculator"> 2*0+10*1+8*2</gadget>
<output>26</output>
26 books;   So  50-26= 
<gadget id="calculator"> 50-26</gadget>
<output>24</output>
24 books are left to distribute among 25-20= 
<gadget id="calculator">25-20</gadget>
<output>5</output>
5 students, these 5 arethe rest who borrowed at least 3 books;   Tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed. Minimum these 4 students could have borrowed is 4 books per student, so total number of books they could have borrowed is 4*3= 
<gadget id="calculator">4*3</gadget>
<output>12</output>
12 books. So the 5th student could have borrowed is  24-12= 
<gadget id="calculator"> 24-12</gadget>
<output>12</output>
12 books.   Answer: 12.
<result>C</result>
In a class of 25 students, 2 students did not borrow any books from the library, 10 students each borrowed 1 book, 8 students each borrowed 2 books, and the rest of the students each borrowed at least 3 books. If the average (arithmetic mean) number of books borrowed per student was 2, what is the maximum number of books that any single student could have borrowed ?