Question

In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 15m high. If the length of the ship is 35 metres, how long is the model ship?

Answer 1

Let x m be the length of the model of the ship. Then, we have:
$$\begin{gathered} 1\mathrm{m}=100\mathrm{cm} \\ \mathrm{Therefore},15\mathrm{m}=1500\mathrm{cm} \\ 35\mathrm{m}=3500\mathrm{cm} \end{gathered}$$

	Length of the mast (in cm)	Length of the ship (in cm)
Actual ship	1500	3500
Model of the ship	9	x

Clearly, if the length of the actual ship is more, then the length of the model ship will also be more.
So, this is a case of direct proportion.
$$\begin{gathered} \mathrm{Now},\frac{1500}{9}=\frac{3500}{x} \\ \Rightarrow x=\frac{3500\times 9}{1500} \\ \Rightarrow x=21\mathrm{cm} \end{gathered}$$
Therefore, the length of the model of the ship is 21 cm.