# If x is inversely proportional to y, and x = 60 when y = 0.5, how do you find x when y = 12?

Mar 31, 2016

$y = \frac{30}{x}$

At $y = 12 \text{; } x = 2 \frac{1}{2} \equiv \frac{5}{2}$

#### Explanation:

Let $k$ be a constant. Then:

$y = k \times \frac{1}{x} = \frac{k}{x}$

It is given that:

$y = \frac{k}{x} \text{ "->" } 0.5 = \frac{k}{60}$

Multiply both sides by 60 giving

$\left(0.5 \times 60\right) = k \times \left(\frac{60}{60}\right)$

But $\frac{60}{60} = 1 \text{ and } 0.5 \times 60 = 30$

$\implies k = 30$

So the relationship is: $y = \frac{30}{x}$
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For $y = 12$ we have

$12 = \frac{30}{x}$

$x = \frac{30}{12} = 2 \frac{6}{12} \to 2 \frac{1}{2}$