108 identical books have a mass of 30 kg. Find

(i) the mass of 150 such books,

(ii) the number of such books that have a mass

of 20 kg.

The mass of 150 books = 41.7kg

The number of books that have mass 20kg = 72 books

Step-by-step explanation:

(I) Number of identical books = 108

Mass of books = 30 kg

Mass of 150 books = ?

Let the mass of 150 books = x kg

To find the mass of 150 books we will use ratio and proportion:

108 books: 30kg = 150 books: x kg

You can also write it like this because ratio can be written in division:

108/30 = 150/x

By cross multiplication:

108x = 150*30

108 x = 4500

Divide both sides by 108

108 x/108 = 4500/108

x = 41.7

Thus the mass of 150 books = 41.7kg

(ii) The number of books that have a mass of 20 kg = ?

Let assume that the number of books of mass 20 kg = y books

We will again use ratio and proportion method.

108 books: 30kg = y: 20kg

We can write it as:

108/30 = y/20

By cross multiplication:

108 * 20 = 30y

2160 = 30y

Divide both the terms by 30

2160/30 = 30y/30

72 = y

Therefore the number of books that have mass 20kg = 72 books ...