in a bookstore, 60 identical books occupy a length of 1.5 m on a shelf. find
(1) the length occupied by 50 such books on a shelf,
(2) the number of such books needed to completely occupy a shelf the is 80 cm long,
In both questions, just use a simple proportion.
#1.
60/50 = 1.5/x
6/5 = 1.5/x
6x = 7.5
x= 1.25 m or 175 cm
#2.
y books/60 books = 80 cm/150 cm , I changed 1.5 m to 150 cm
y/60 = 8/15
15y = 480
y = 32 ,
32 books
Because 1.5 meters divided by 60 is 2.5 centimeters all you need to do to answer one is multiple 2.5 centimeters by 50
So, if you divide 1.5 meters by 60 you get 2.5 centimeters so in order to answer number 2 you need to divide 80 by 2.5
hope this helps <3
To find the answers, we can calculate the length occupied by each book and then use that information to solve the questions.
Let's start by calculating the length of a single book:
Length occupied by 60 books = 1.5 m
Length of 1 book = (1.5 m) ÷ 60
Length of 1 book = 0.025 m or 2.5 cm
Now we can use this information to solve the questions:
(1) To find the length occupied by 50 books on a shelf:
Length of 50 books = (Length of 1 book) × 50
Length of 50 books = 0.025 m × 50
Length of 50 books = 1.25 m
Therefore, 50 such books will occupy a length of 1.25 meters on a shelf.
(2) To find the number of books needed to completely occupy a shelf that is 80 cm long:
Length of the shelf = 80 cm
Number of books = (Length of the shelf) ÷ (Length of 1 book)
Number of books = 80 cm ÷ 0.025 m
Number of books = 320
Therefore, 320 such books would be needed to completely occupy a shelf that is 80 cm long.
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 ≈ 48 / 1.5
x ≈ 32
Therefore, you would need approximately 32 books to completely occupy an 80 cm long shelf.