Question

If x varies inversely as y, and x=27 when y=6 find x when y=2

Answer 1

For this case we have that the inverse variation is defined as:

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

Where:

k: It is the constant of proportionality

According to the statement we have:

$x = 27\\y = 6\\6 = \frac {k} {27}$

We find the constant of proportionality:

$k = 27 * 6\\k = 162$

Then we find the value of x when $y = 2$:

$2 = \frac {162} {x}\\x = \frac {162} {2}\\x = 81$

Answer:

$x = 81$