Bookshelf

A bookshelf is 36 inches long and contains n books each w inches thick. If each book were half an inch thinner, the shelf would hold six more of the same book. What is n/w?
Source: NCTM Mathematics Teacher, February 2006

SOLUTION
nw=36\qquad\qquad\qquad\qquad (1)
(n+6)(w-1/2)=36\qquad (2)
Substitute the value of w from Eq.(1) into Eq.(2)
(n+6)(36/n-1/2)=36
36-n/2+216/n-3=36
Simplify
n^2+6n-432=0
(n+24)(n-18)=0
n=-24 (extraneous solution) or n=18
Substitute the value of n into Eq.(1)
18w=36
w=2
n/w=18/2=9

Answer: 9

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About mvtrinh

Retired high school math teacher.
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