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Sophie is reading a book. She notices that a few pages are missing. The sum of the numbers of the missing pages is 98.
If a sheet of paper in a book has two page numbers (one on each side), how many sheets are missing from Sophie’s book?
Each sheet of paper in a book has two pages (one on each side). We need to find how many sheets are missing if the sum of the missing page numbers is 98.
ReplyDeleteStep 1: Understanding the sum of two consecutive pages
Each missing sheet contains two consecutive pages. If a sheet has pages n and n+1, their sum is:
n + (n+1) = 2n + 1
This means that the sum of any missing sheet’s pages is always an odd number.
Step 2: Finding how many sheets are missing
Since 98 is an even number, it must be made up of multiple sums of odd numbers. The sum of two odd numbers is always even, so the number of missing sheets must be even.
Step 3: Checking possibilities
Let’s check if two sheets can be missing:
A missing sheet with pages (23,24) has a sum of 47.
Another missing sheet with pages (25,26) has a sum of 51.
47 + 51 = 98.
So, the missing pages are (23,24) and (25,26).
Final Answer:
Sophie is missing 2 sheets.