Respuesta :
Answer:
The total number of bookmarks Min will need is 700.
Step-by-step explanation:
The book consists of 10000 pages.
The bookmarked pages are of 4-digit page numbers. That is the page numbers of the bookmarked pages are in the range 1000 - 9999.
Also, the sum of the thousands digit and the units digit is 7.
So the possible page numbers are of the form:
[tex]1\ \_\ \_\ 6\\2\ \_\ \_\ 5\\3\ \_\ \_\ 4\\4\ \_\ \_\ 3\\5\ \_\ \_\ 2\\6\ \_\ \_\ 1\\7\ \_\ \_\ 0[/tex]
Thus, there are 7 options to to satisfy the condition that the sum of the thousands digit and the units digit is 7.
Now consider the first option, i.e. [tex]1\ \_\ \_\ 6[/tex]
The middle two places can be occupied by any number between 0 - 9, i.e. there are [tex]10\times10=100[/tex] such numbers that has 1 in the thousandth place and 6 in the units place.
Similarly for all the remaining options the middle two places can be occupied in 100 ways.
The possible number of of bookmarks is = [tex]7\times100=700[/tex]
Thus, the total number of bookmarks Min will need is 700.
