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12 Jun 2008, 14:32
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In a clss of 30 students, 2 students did not borrow any books from the library. 12 students each borrowed 1 book, 10 each borrowed 2 books, and the rest of the students each borowed at least 3 books. If the average number of books borrowed per student was 2, what was the maximum number of books that any single student could have borrowed?
Can someone please help. Thanks.
Can someone please help. Thanks.
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Updated on: 13 Jun 2008, 06:33
Originally posted by brokerbevo on 12 Jun 2008, 14:44.
Last edited by brokerbevo on 13 Jun 2008, 06:33, edited 1 time in total.
Last edited by brokerbevo on 13 Jun 2008, 06:33, edited 1 time in total.
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You first need to set up the average for what is known:
2 students - 0 books
12 students - 1 book
10 students - 2 books
rest (or 6) - at least 3 books
So, the only way to maximize the books borrowed of 1 student is to minimize the remaining books borrowed from the other unknown students. Since there are 6 students left, we will minimize the books borrowed of 5 of these students (the lowest possible amount being 3 books) and maximize the last remaining student's books (which we will call "x")
Set up the average formula:
\([2(0) + 12(1) + 10(2) + 5(3) + 1(x)]/30 = 2\)
solve for x
= 13
12 Jun 2008, 14:49
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Let's understand the question:
Number Students Books
2 0
12 1
10 2
6 >=3
The average is 2 books, so we know that the total number of borrowed books is 2*30 = 60
The know the maximum number os books a student could have taken, lets suppose that, from the group that took 3 or more books, 5 students took 3, and only 1 took more.
So we have: 12*1+10*2+5*3+1*x = 60 / x = 60-47
x = 13
Number Students Books
2 0
12 1
10 2
6 >=3
The average is 2 books, so we know that the total number of borrowed books is 2*30 = 60
The know the maximum number os books a student could have taken, lets suppose that, from the group that took 3 or more books, 5 students took 3, and only 1 took more.
So we have: 12*1+10*2+5*3+1*x = 60 / x = 60-47
x = 13
