Hiram's algebra notes are 50 pages long and are printed on 25 sheets of paper; the first sheet contains pages 1 and 2, the second sheet contains pages 3 and 4, and so on. One day he leaves his notes on the table before leaving for lunch, and his roommate decides to borrow some pages from the middle of the notes. When Hiram comes back, he discovers that his roommate has taken a consecutive set of sheets from the notes and that the average (mean) of the page numbers on all remaining sheets is exactly 19. How many sheets were borrowed?
Each sheet contains 2 pages
So...let x be the number of sheets that were "borrowed"
So.....the number of pages that remain = 50 - 2x
Taking the average of these remaining pages = 19 ......so....
( 50 - 2x ) / 2 = 19
50 - 2x = 38
50 - 38 = 2x
12 = 2x
x = 6 sheets were "borrowed"