JAMB 1988 · UME · Q14

Variation

If $x$ varies inversely as the cube root of $y$ , and $x = 1$ when $y = 8$ , find $y$ when $x = 3$ .

Worked solution (try it first)

Inverse variation means $x\sqrt[3]{y}$ is constant.
With $x = 1$ , $y = 8$ : $k = 1 \times 2 = 2$ .
When $x = 3$ : $3\sqrt[3]{y} = 2$ , so $\sqrt[3]{y} = \frac23$ .
Cube both sides: $y = \left(\frac23\right)^3 = \frac{8}{27}$ , option C.

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