
For our third problem, y would be equal to 8. Great work for getting that one

correct. You might have had trouble with the set up, so let's see how we can do

that. We know x varies directly with y, so they should be directly across from

each other in our proportion. But for z, x varies inversely, so z should appear

in the denominator. I want to start by plugging in the values of my first case

first, x1 is 5, y1 is 5, and z1 is 3. In my second case, I don't know this value

of y. It's what we're looking for. So I'd be sure to list y2 as my variable. Or

just y. The second value for x is 6, and the second value for z is positive 4.

Now we have an equation we can solve with a rational expression. We multiply

these two fractions together, to get 20 divided by 3y. Then we crossmultiply to

get 15 y times 120. And finally we divide by 15 to get y is equal to 8. Again, I

think the setup to this problem is probably the hardest. You want to make sure

that when you're varying directly, things are across from one another. Whereas

if things vary inversely, they're diagonally across from one another.