Question

Suppose 2 kg of sugar contains 9 × 10⁶ crystals.

How many sugar crystals are there in

1. 5 kg of sugar?
2. 1.2 kg of sugar?

Answer 1

i. Let the number of sugar crystals in 5 kg of sugar be x.

The given information, in the form of a table, is as follows:

Amount of sugar (in kg)	2	5
Number of crystals	9 × 106	x

The amount of sugar and the number of crystals it contains are directly proportional to each other. Therefore, we obtain

⇒ `2/(9xx10^6) = 5/x`

⇒ x = `(5xx9xx10^6)/2`

⇒ x = `(5xx9xx100000)/2`

⇒ x = 2.25 × 10⁷

Hence, the number of sugar crystals is 2.25 × 10⁷

ii. Let the number of sugar crystals in 1.2 kg of sugar be y. The given information, in the form of a table, is as follows:

Amount of sugar (in kg)	2	1.2
Number of crystals	9 × 106	y

⇒ `2/1.2 = (9xx10^6)/y`

⇒ `y = (1.2xx9xx10^6)/2`

⇒ y = 5.4 × 10⁶

Hence, the number of sugar crystals is 5.4 x 10⁶