Question

If y is in direct variation with x and x = 18 when y = 15 then find
(i) The value of y when x = 4.5
(ii) The value of x when y = 2.5

Answer 1

$$\begin{gathered} y\alpha x \\ \therefore y=kx(H\mathrm{ere},k\mathrm{is}a\mathrm{constant}.) \\ \Rightarrow 15=18k \\ \Rightarrow k=\frac{15}{18}=\frac{5}{6} \\ \Rightarrow y=\frac{5}{6}x(T\mathrm{his}\mathrm{is}\mathrm{the}\mathrm{equation}\mathrm{of}\mathrm{variation}.) \\ \left(\mathrm{i}\right)y=\frac{5}{6}\times 4.5\left(\because x=4.5\right) \\ \therefore y=3.75 \\ \left(\mathrm{ii}\right)2.5=\frac{5}{6}\times x\left(\because y=2.5\right) \\ \Rightarrow x=\frac{2.5\times 6}{5} \\ \Rightarrow x=3 \end{gathered}$$