If y varies inversely with x, and the constant of variation is 24, find y when x = 8.

First, write the general form for inverse variation.

We know the constant of variation, so plug in that value for k.

Now solve for y when x = 8.

y = 3

Given that x and y vary inversely, write the equation relating x and y if x = 3 when y = 10.

First, write the general form for inverse variation.

Plop in our known values for x and y to track down the elusive k.

Solve for k.

k = 30

There you are, little buddy. That means our equation is:

Given that x and y vary inversely, and that y = 17 when x = 17, find y when x = 0.5.

As usual, we kick things off by writing the general form for inverse variation.

Now plug in those x- and y-values to find k.

Solve for k:

k = 289

Bingo. Now we know our equation is:

For the finishing touch, plug in x = 0.5 and solve for y.

y = 578