JAMB 1983 · UME · Q23

If $w$ varies inversely as $V$ and $u$ varies directly as $w^3$ , find the relationship between $u$ and $V$ , given that $u = 1$ when $V = 2$ .

Worked solution (try it first)

$w$ varies inversely as $V$ , so $w = \dfrac{c}{V}$ for some constant $c$ .
$u$ varies as $w^3$ , and $w^3 = \dfrac{c^3}{V^3}$ , so $u$ varies inversely as $V^3$ : $u = \dfrac{k}{V^3}$ .
Put in $u = 1$ , $V = 2$ : $1 = \dfrac{k}{8}$ , so $k = 8$ and $u = \dfrac{8}{V^3}$ , option E.