To find the length occupied by a specific number of books on a shelf, we can use the concept of proportions.
Let's set up a proportion using the given information:
Length of 60 books = 1.5 m
Length of x books = ?
(1) To find the length occupied by 50 books on a shelf, we will cross-multiply:
60 books / 1.5 m = 50 books / x
(60 * x) = (1.5 * 50)
By cross-multiplying, we can find the value of x:
60x = 75
x = 75 / 60
x = 1.25 m
Therefore, 50 books will occupy a length of 1.25 meters on the shelf.
(2) To find the number of books needed to completely occupy a shelf that is 80 cm (0.8 m) long, we will set up a proportion again:
Length of 60 books = 1.5 m
Length of x books = 0.8 m
60 books / 1.5 m = x books / 0.8 m
(60 * 0.8) = (1.5 * x)
By cross-multiplying, we can find the value of x:
48 = 1.5x
x โ 48 / 1.5
x โ 32
Therefore, you would need approximately 32 books to completely occupy an 80 cm long shelf.