1. An empty bookcase has 6 shelves, and each shelf can hold no more than 50 books. You want to arrange 60 books in the bookcase so that the same number of books is on each shelf used. a. List the factors of 60. b. List the factors of 60 that represent the number of books that could be on each shelf. c. How many different arrangements of books are possible? d. What are the possible arrangements of the books? e. Which arrangement uses all of the shelves?
+23254 The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Since only 50 books can be on a shelf, the usable factors are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30
Using 6 shelves: 6 x 10 = 60
Using 5 shelves: 5 x 12 = 60
Using 4 shelves: 4 x 15 = 60
Using 3 shelves: 3 x 20 = 60
Using 2 shelves: 2 x 30 = 60
+23254 The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Since only 50 books can be on a shelf, the usable factors are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30
Using 6 shelves: 6 x 10 = 60
Using 5 shelves: 5 x 12 = 60
Using 4 shelves: 4 x 15 = 60
Using 3 shelves: 3 x 20 = 60
Using 2 shelves: 2 x 30 = 60
