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JAMB Mathematics 2019 Paper

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Question : 31

Total: 73

If P varies inversely as the square root of q, where p = 3 and q = 16, find the value of q when p = 4.

12
8
9
16

Solution:

Concept:

Inverse variation with a square root means

p = \frac{k}{\sqrt{q}}

, where

k

is the constant of proportionality.

Explanation:

Given

p \propto \frac{1}{\sqrt{q}}

, we write

p = \frac{k}{\sqrt{q}}

.

Substitute

p = 3

and

q = 16

:

3 = \frac{k}{\sqrt{16}}

.

Since

\sqrt{16} = 4

, we get

3 = \frac{k}{4}

, so

k = 12

.

The relation becomes

p = \frac{12}{\sqrt{q}}

.

Now set

p = 4

:

4 = \frac{12}{\sqrt{q}}

.

Multiply both sides by

\sqrt{q}

:

4\sqrt{q} = 12

, so

\sqrt{q} = 3

.

Squaring both sides gives

q = 3^2 = 9

.

Answer:

q = 9

(Option C).

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