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# If x is inversely proportional to y and x = 2$$\frac{1}{2}$$ when y = 2, find x ...

### Question

If x is inversely proportional to y and x = 2$$\frac{1}{2}$$ when y = 2, find x if y = 4

### Options

A) 4

B) 5

C) 1$$\frac{1}{4}$$

D) 2$$\frac{1}{4}$$

The correct answer is C.

### Explanation:

x $$\alpha$$ $$\frac{1}{y}$$ .........(1)
x = k x $$\frac{1}{y}$$ .........(2)
When x = 2$$\frac{1}{2}$$
= $$\frac{5}{2}$$, y = 2
(2) becomes $$\frac{5}{2}$$ = k x $$\frac{1}{2}$$
giving k = 5
from (2), x = $$\frac{5}{y}$$
so when y =4, x = $$\frac{5}{y}$$ = 1$$\frac{1}{4}$$

## Dicussion (1)

• x $$\alpha$$ $$\frac{1}{y}$$ .........(1)
x = k x $$\frac{1}{y}$$ .........(2)
When x = 2$$\frac{1}{2}$$
= $$\frac{5}{2}$$, y = 2
(2) becomes $$\frac{5}{2}$$ = k x $$\frac{1}{2}$$
giving k = 5
from (2), x = $$\frac{5}{y}$$
so when y =4, x = $$\frac{5}{y}$$ = 1$$\frac{1}{4}$$

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