The Book Problem Mr. Kato had some paperback books that he no longer wanted. Rat

Question

The Book Problem Mr. Kato had some paperback books that he no longer wanted. Rather than throw them away, he put them in a box and took them to school for his students. At the end of each class period, he let the students in that class take a fraction of the books that were still left in the box. He told the 1" period class that they could take 1/6 of the books. The second period class was allowed to take 1/5 of the books that were left. The 3rd period class took of the remaining books. 1/3 of the books that were still left were taken by the 4th period class. Thefifth period class took '% of the remaining books. This left 1e4 books for the sixth period. The students took all the books. How many books did Mr. Kato start with?

Explanation / Answer

Let the number of books be x.

After 1st period, the number of books left = x - x/6 = 5x/6 = (5/6) x.

After 2nd period, the number of books left = (5/6)x - (5/6) x/5 = (4/5) (5/6) x.

After 3rd period, the number of books left = (4/5) (5/6) x - (4/5) (5/6) x/4 = (3/4) (4/5) (5/6) x

After 4th period, the number of books left = (2/3) (3/4) (4/5) (5/6) x

After 5th period, the number of books left = (1/2) (2/3) (3/4) (4/5) (5/6) x = (1/6) x

Given (1/6) x = 14

=> x = 14 * 6 = 84.

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