If y varies directly with x and inversely with z, and y = 25 when x = 10 and z = 2, find y when x = 18 and z = 9.

First, write the general form for combined variation:

Plug in the given values and solve for k:

25 = 5k

k = 5

Hey, lookie there: we've got a general equation:

Now find y when x = 18 and z = 9:

y = 5(2) = 10

If y varies directly with x and inversely with z, and y = 12 when x = 100 and z = 25, find y when x = 36 and z = 12.

Let's get down to basics. The general form for combined variation is:

We know y = 12 when x = 100 and z = 25, so throw all that into the formula like fruit into a blender.

Hit "blend" to get our delicious k-smoothie.

12 = 4k

k = 3

Now plug our k-value into the general equation:

Final step: find y when x = 36 and z = 12:

y = 3(3) = 9

Given the combined variation equation , find x when y = 2 and z = 10.

This is just your basic, run-of-the-mill algebra problem. We wanna solve for x, so multiply both sides by z:

yz = 4x

Now plug in y = 2 and z = 10:

2(10) = 4x

20 = 4x

And solve that baby for x:

x = 5