SOLUTION: Two pages that face each other in a book have 288 as the sum of their page numbers. What are the page numbers?

Question 509194: Two pages that face each other in a book have 288 as the sum of their page numbers. What are the page numbers?
Found 3 solutions by solver91311, Alan3354, Edwin McCravy:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Impossible unless the pages are numbered with fractions.

Let represent the smaller page number. Then the next page has to be because if the pages are facing, their page numbers must differ by one.

John

My calculator said it, I believe it, that settles it

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Two pages that face each other in a book have 288 as the sum of their page numbers. What are the page numbers?
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143 + 144 = 287
144 + 145 = 289
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They have to be 143.5 & 144.5, the new method of page numbering.
It's not possible with integers.

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!

That's impossible because any two pages that face each other in a book always consist of an even numbered page on the left and an odd-numbered page on the right. So 288 can't possibly be the sum of their page numbers because the sum of an odd number and an even number is ALWAYS an odd number, never an even number. Yet 288 is an even number. So this cannot be. Your teacher will have to agree. If the sum were 287 instead of 288, the problem would be possible. We would let n = the page number of the page on the left and let n + 1 = the page number of the facing page on the right. then the equation would be n + (n + 1) = 289 n + n + 1 = 288 2n + 1 = 288 2n = 288 n = 144 So the number of the page on the left is n=144 and the page number on the right is n+1=144+1=145. If you try that with the sum of 288, you get the ridiculous answer that the page on the left is numbered and the one facing it is numbered . No book has pages numbered with fractions! Edwin

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