Question

If x and y vary inversely as each other and
(i) x = 3 when y = 8, find y when x = 4
(ii) x = 5 when y = 15, find x when y = 12
(iii) x = 30, find y when constant of variation = 900.
(iv) y = 35, find x when constant of variation = 7.

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{Since}x\mathrm{and}y\mathrm{vary}\mathrm{inversely},\mathrm{we}\mathrm{have}: \\ xy=k \\ \mathrm{For}x=3\mathrm{and}y=8,\mathrm{we}\mathrm{have}: \\ 3\times 8=k \\ \Rightarrow k=24 \\ \mathrm{For}x=4,\mathrm{we}\mathrm{have}: \\ 4y=24 \\ \Rightarrow y=\frac{24}{4} \\ =6 \\ \therefore y=6 \\ \left(\mathrm{ii}\right)\mathrm{Since}x\mathrm{and}y\mathrm{vary}\mathrm{inversely},\mathrm{we}\mathrm{have}: \\ xy=k \\ \mathrm{For}x=5\mathrm{and}y=15,\mathrm{we}\mathrm{have}: \\ 5\times 15=k \\ \Rightarrow k=75 \\ \mathrm{For}y=12,\mathrm{we}\mathrm{have}: \\ 12x=75 \\ \Rightarrow x=\frac{75}{12} \\ =\frac{25}{4} \\ \therefore x=\frac{25}{4} \\ \left(\mathrm{iii}\right)\mathrm{Given}: \\ x=30\mathrm{and}k=900 \\ \therefore xy=k \\ \Rightarrow 30y=900 \\ \Rightarrow y=\frac{900}{30} \\ =30 \\ \therefore y=30 \\ \left(\mathrm{iv}\right)\mathrm{Given}: \\ y=35\mathrm{and}k=7 \\ \mathrm{Now},xy=k \\ \Rightarrow 35x=7 \\ \Rightarrow x=\frac{7}{35} \\ =\frac{1}{5} \\ \therefore x=\frac{1}{5} \end{gathered}$$