In a class of 20 students, 2 students did not borrow any books from the library, 8 students each borrowed 1 book, 5 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 ? Pick one:
A) 3
B) 5
C) 10
D) 13
E) 15
The average number of books per student was 2means that total of   2*20= 
<gadget id="calculator">  2*20</gadget>
<output>40</output>
40 books were borrowed;   2+8+5= 
<gadget id="calculator">2+8+5</gadget>
<output>15</output>
15 students borrowed total of  2*0+8*1+5*2= 
<gadget id="calculator"> 2*0+8*1+5*2</gadget>
<output>18</output>
18 books;   So  40-18= 
<gadget id="calculator"> 40-18</gadget>
<output>22</output>
22 books are left to distribute among 20-15= 
<gadget id="calculator">20-15</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 3 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  22-12= 
<gadget id="calculator"> 22-12</gadget>
<output>10</output>
10 books.   Answer: 10.
<result>C</result>
In a class of 20 students, 2 students did not borrow any books from the library, 8 students each borrowed 1 book, 5 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 ?