Question

Suppose $2kg$ of sugar contains $9\times {10}^6$ crystals.

How many sugar crystals are there in (i) $5kg$ of sugar (ii) $1.2kg$ of sugar

Answer 1

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

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

$\begin{array}{ccc}\text{Amount of Sugar (in kg)}& 2& 5\\ \text{Number of crystals}& 9\times {10}^6& x\end{array}$

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

$\frac{2}{9\times {10}^6}=\frac{5}{x}$

$\therefore x=\frac{5\times 9\times {10}^6}{2}=2.25\times {10}^7$

Hence, the number of sugar crystals is $2.25\times {10}^7.$

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

$\begin{array}{ccc}\text{Amount of Sugar (in kg)}& 2& 1.2\\ \text{Number of crystals}& 9\times {10}^6& y\end{array}$

$\frac{2}{9\times {10}^6}=\frac{1.2}{y}$

$\therefore y=\frac{1.2\times 9\times {10}^6}{2}=5.4\times {10}^6$

Hence, the number of sugar crystals is $5.4\times {10}^6.$