A pile of 108 identical books has a mass of 30 kg. Find (a)the mass of 150 books and (b)the number of books that has a mass of 20 kg.
Use proportions. Cross multiply and solve for x.
108/30 = 150/x
108/30 = x/20
To find the mass of 150 books, we can use the concept of proportion.
Given that a pile of 108 identical books has a mass of 30 kg, we can set up a proportion to find the mass of 150 books.
Let's create the proportion:
Mass of 108 books / Number of 108 books = Mass of 150 books / Number of 150 books
From the given information, we know that the mass of 108 books is 30 kg. We need to find the mass of 150 books.
Setting up the proportion:
30 kg / 108 books = Mass of 150 books / 150 books
Now, let's solve for the unknown mass of 150 books. Cross-multiplying the proportion, we get:
(30 kg)(150 books) = (108 books)(Mass of 150 books)
To solve for the mass of 150 books, divide both sides of the equation by 108 books:
(30 kg)(150 books) / 108 books = Mass of 150 books
Calculating the mass of 150 books, we get:
Mass of 150 books ≈ 41.67 kg
Therefore, the mass of 150 books is approximately 41.67 kg.
To find the number of books that have a mass of 20 kg, we can set up another proportion.
Let's create the proportion:
Mass of 30 kg / Number of 108 books = Mass of 20 kg / Number of books with 20 kg mass
We already know the mass of 30 kg corresponds to 108 books. Now, we need to find the number of books with a mass of 20 kg.
Setting up the proportion:
30 kg / 108 books = 20 kg / Number of books with 20 kg mass
Now, let's solve for the unknown number of books with a mass of 20 kg. Cross-multiplying the proportion, we get:
(30 kg)(Number of books with 20 kg mass) = (108 books)(20 kg)
To solve for the number of books with a mass of 20 kg, divide both sides of the equation by 20 kg:
(30 kg)(Number of books with 20 kg mass) / 20 kg = 108 books
Simplifying the equation:
1.5(Number of books with 20 kg mass) = 108 books
To solve for the number of books with a mass of 20 kg, divide both sides of the equation by 1.5:
(Number of books with 20 kg mass) = 108 books / 1.5
Calculating the number of books with a mass of 20 kg, we get:
Number of books with 20 kg mass ≈ 72 books
Therefore, the number of books that have a mass of 20 kg is approximately 72 books.