Algebra II direct, inverse, and joint variation?

Question

I need help setting up the formula for inverse and joint variation.

Inverse: y=k/x
joint: y=kxz

I know how to do "y varies ... as" problems, but I'm wondering about "x varies ... as" problems. I'm not asking to do the work, but for help setting up the equation.

-If x varies inversely as y and y=40 when x=4, find x when y=20.

-Suppose x varies jointly as y and z. If x=50 when y=2 and z=4, find x when y=6 and z=10.

Answer 1

You just need to rewrite the problem:

Instead of y=k/x

you need to write it as: x=k/y

Now, you can work out the problem.

4 = k/40
160 = k

Now, plug it back in.

x = k / y
x = 160 / 20
x = 8


You can do the same thing for the joint problem.

Instead of y=kxz

It will be x=kyz.

Good luck!

Mysstere