## shadmanr163 2 years ago Are there any common tricks with inverse and direct variation? Examples would be very helpful for me.

Let's say I was able to measure productivity $$w$$, profit $$p$$, and cost of materials $$c$$ quantitatively. A reasonable model for an explicitly simple system would be:$p=\frac{w}{c}$Now, which variables vary directly, and which vary indirectly? Tell me what you think. Even if it's wrong.

Vary Directly-c Vary indirecly-w I am not sure.

Alright, so as $$p$$ increases in$p=\frac{w}{c}$either $$w$$ is getting higher, or $$c$$ is getting lower, or both. For instance, if $$p=2$$, $$w=6$$, and $$c=3$$, what are possible values of $$w,c$$ if I increased $$p=4$$?

6=36/6

Very good. You noticed that $$w$$ increased (by a larger margin than $$c$$)? Now, returning to the previous question, what if I reduced $$p=1$$?

if reduced by one then 1=infinite no of solutions?

Yes, there are an infinite number of solutions. I'm asking what are possible solutions.

like 6/6

Yup. Noticed now how $$c$$ increased by a larger margin than $$w$$? So what do you think: does $$p$$ increase and decrease directly or inversely with $$c$$ and $$w$$?

inversely

Not both. Which to which? If I increase $$p$$, $$w$$ generally grows larger and $$c$$ smaller, so the number $$w/c$$ is larger. If I decrease $$p$$, $$w$$ generally grows smaller, and $$c$$ larger, so $$w/c$$ grows smaller. Do you understand?

Yeah! Thanks a lot so much. :-) Now I understand

So, final test. Does $$c$$ vary inversely or directly with $$p$$? What about $$w$$?

Hey, I invested time into this. I want to see you actually learned something. :P

Just, Hold on a bit I will get to it...

@myininaya I know you're an actual teacher, you might be better here. :P