# algebra

posted by Neil

John has 36 books in his locker.
He has text books,library books, and telephone books. How many books of each kind does he have if:
lib + tel= 2x text books and
text + tel = 3x lib books

I think it'd be easier to let T,L and B denote text books, library books and telephone books. Then
(1) L + B = 2T
(2) T + B = 3L
We also know
(3) T + L + B = 36
So from (1)
L = 2T - B now substitute into (3) to get
T +2T - B + B = 36 or
3T = 36 so
T = 12, therefore L + B = 24 or L = 24 - B
Then from (2)
12 + B = 3(24 - B) so
12 + B = 72 - 3B and
4B = 60 or B = 15
You should be able to figure out what L is and verify if the answers are correct.

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