# If Y varies inversely as twice x and when x = 3, y = 8 how do you find y when x = 2?

May 29, 2017

When $x = 2 , y = 12$

#### Explanation:

• Write the statement as an inverse proportion first:
$y \propto \frac{1}{2 x}$
• Change to an equation using a constant $k$

$y = \frac{k}{2 x} , \text{ }$ which can be written as $\text{ } k = 2 x \times y$

• Use the values given to find a value for $k$
$k = \left(2 \times 3\right) \times 8 = 48$

• Use the values for $k \mathmr{and} x$ to find $y$.

$y = \frac{k}{2 x} = \frac{48}{2 \times 2}$

$= \frac{48}{4} = 12$

May 29, 2017

y = 12

#### Explanation:

Here $y \propto \frac{1}{2 x}$

or, $y = k . \frac{1}{2 x}$ ..............(i)

put x = 3 & y = 8 we get, $8 = k . \frac{1}{2 \times 3}$

$\Rightarrow k = 48$

Again putting the value of k & x in (i) to find 'y'

$\Rightarrow y = 48. \frac{1}{2 \times 2}$

$\Rightarrow y = 12$