Diana P.

asked • 05/10/17

A book has one page missing. The sum of the digits of the remaining pages is equal to 10,000. ow many pages are in the book and which page is missing?

 A book has one page missing. the sum of the digits of the remaining pages is equal to 10,000. How many pages in the book and what page is missing?

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Mark M. answered • 05/10/17

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10000 = n/2)(2 + (n - 1))
10000 = (n/2)(n + 1)
20000 = n(n + 1)
20000 = n2 + n
0 = n2 + n - 20000
 
Can you solve for n? 
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Diana P.

It has been a long time since I did algebra, can you complete the solution so I can mull it over and try to understand?  I really have no idea how to isolate the n and solve for it's value.
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05/10/17

Mark M.

Since the coefficient on the linear term is 1, we are looking for two numbers whose sum is 1 and whose product whose 20000. The easiest way is to look at the square root of 20000. √20000 = 141.42.
Let's see was the sum of 141 page is.
S141 = (141/2)(2 + 141 - 1)
S141 = (141/2)(142)
S141 = (141)(72)
S141 = 10,152
 
So the book has 141 pages and page 152 is missing. 
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05/10/17

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