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! 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.
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
