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JAMB Mathematics 2010 Paper

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Question : 32

Total: 49

If x is inversely proportional to y and x = 2

\frac{1}{2}

when y = 2, find x if y = 4

4
5
1 $\frac{1}{4}$
2 $\frac{1}{4}$

Solution:

Concept:

Inverse proportion means the product of

x

and

y

is constant.

Explanation:

Since

x

is inversely proportional to

y

, write

x = \frac{k}{y}

, where

k

is the constant of proportionality.

Given

x = 2\frac{1}{2} = \frac{5}{2}

when

y = 2

.

Substitute into

x = \frac{k}{y}

:

\frac{5}{2} = \frac{k}{2}

Multiply both sides by

2

:

k = 5

So the relationship is

x = \frac{5}{y}

.

Now find

x

when

y = 4

:

x = \frac{5}{4} = 1\frac{1}{4}

Answer:

x = 1\frac{1}{4}

, which is option C.

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