Question

Suppose 2 kg of sugar contains 9 x 106 crystals. How many sugar crystals are there in (i) 5 kg of sugar? (ii) 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
\(\frac{2 }{ (9 × 10^6)} = \frac{5 }{ x}\)
\(x = \frac{(9 × 10^6× 5) }{ 2}\)
\(x = 22.5 × 10^7\)
Hence there are 2.25 × 10⁷ crystals.
(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

\(\frac{2}{(9 × 10^6)} = \frac{1.2}{y}\)
\(2 × y = 9 × 10^6 × 1.2\)
\(y = \frac{(9 × 10^6× 1.2)}{2}\)
\(y = 5.4 × 10^6\)
Hence there are 5.4 × 10⁶ crystals.