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WAEC Mathematics 2017 Paper

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Question : 2

Total: 49

If x varies inversely as y and y varies directly as z, what is the relationship between x and z?

x $\alpha$ z
x $\alpha$ $\frac{1}{z}$
a $\alpha$ z $^{2}$
x $\alpha$ $\frac{1}{z^{2}}$

Solution:

Concept:

Combining two variation relations: inverse variation and direct variation.

Explanation:

Since

x

varies inversely as

y

, we write:

x \propto \frac{1}{y}

So,

x = \frac{k}{y}

, where

k

is a constant.

Since

y

varies directly as

z

, we write:

y \propto z

So,

y = mz

, where

m

is a constant.

Substitute

y = mz

into

x = \frac{k}{y}

:

x = \frac{k}{mz}

Since

k

and

m

are constants,

\frac{k}{m}

is a constant.

Therefore,

x \propto \frac{1}{z}

.

Answer:

x \propto \frac{1}{z}

Correct option: B.

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