Math CentralQuandaries & Queries


Question from Julie, a parent:

a bookshelf is 36 inches long and contains (x) books each (n) inches thick. If each book half an inch thinner, the shelf would hold six more of the same book. What is x/n

Hi Julie,

If each books is n inches thick and there are x books that's a total of xn inches which you know is 36 inches. Hence

xn = 36.

If each book is half an inch thinner they are each n - 1/2 inches thick. That would allow for x + 6 books on the shelf. The shelf is 36 inches long so

(x + 6)(n - 1/2) = 36.

By the first equation n = 36/x. Substitute this into the second equation and solve for x.

I hope this helps,

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