Question

The amount of extension in an elastic string varies directly as the weight hung on it. If a weight of 150 gm produces an extension of 2.9 cm, then what weight would produce an extension of 17.4 cm?

Answer 1

Let x gm be the weight that would produce an extension of 17.4 cm.

Weight (in gm)	150	x
Length (in cm)	2.9	17.4

$$\begin{gathered} \mathrm{Since}\mathrm{the}\mathrm{amount}\mathrm{of}\mathrm{extension}\mathrm{in}\mathrm{an}\mathrm{elastic}\mathrm{string}\mathrm{and}\mathrm{the}\mathrm{weight}\mathrm{hung}\mathrm{on}\mathrm{it}\mathrm{are}\mathrm{in}\mathrm{direct}\mathrm{variation},wehave: \\ \frac{150}{x}=\frac{2.9}{17.4} \\ \Rightarrow 17.4\times 150=2.9\times x \\ \Rightarrow x=\frac{17.4\times 150}{2.9} \\ =\frac{2610}{2.9} \\ =900 \\ \mathrm{Thus},\mathrm{the}\mathrm{required}\mathrm{weight}\mathrm{will}\mathrm{be}900\mathrm{gm}. \end{gathered}$$