How can i solve joint proportion?

[the legion]

I am currently doing aops introduction to algebra book and I can't figure out how to solve joint proportion or some ppl call it joint variation. I don't which values should i substitute for the formula, z=kxy. I don't which value should i substitute into z to the word problems. I can get through direct proportion and inverse proportion fine but when i got to the word problems i started to struggle. I couldn't figure out which value's to substitute in this word problem:

Five woodchucks would chuck eight pieces of wood in two hours if a woodchuck could chuck wood. How much wood would one woodchuck chuck if one woodchuck would chuck wood for one day?

Five chickens eat 10 bags of scratch in 20 days. How long does it take 18 chickens to eat 100 bags of scratch?

can someone please try explain this to me in simple math...?? and please tell me where i can find more problems like this so i can practice.

 

[PAllen]

I don't know about the terminology you use, or methods you've been taught, but for understanding:

Break it down, a basic approach to many problems. Ask yourself:

<something > chucks 8 in two hours

so <something> chucks what per hour?

Then look at the <something> and answer the rate for one woodchuck. Then work from there for the rest of the problem.

 

[the legion]

I don't know about the terminology you use, or methods you've been taught, but for understanding:

Break it down, a basic approach to many problems. Ask yourself:

<something > chucks 8 in two hours

so <something> chucks what per hour?

I don't know about the terminology you use, or methods you've been taught, but for understanding:

Break it down, a basic approach to many problems. Ask yourself:

<something > chucks 8 in two hours

so <something> chucks what per hour?

Then look at the <something> and answer the rate for one woodchuck. Then work from there for the rest of the problem.

Then look at the <something> and answer the rate for one woodchuck. Then work from there for the rest of the problem.

k, ill tell u wht hppend nw :

take this problem for an example :

Five chickens eat 10 bags of scratch in 20 days. How long does it take 18 chickens to eat 100 bags of scratch?

Now this is another word problem that i am having problem with. When i look at the solution it ends up with this:

(Time in days) (Number of chickens)

--------------------------------------------

(Bags of Scratch)

Now I don't understand how they ended up with those two equations. I mean, if i double the amount of chickens, the amount of scratch eaten goes up. I understand, how that equation works. Now I don't understand why did they put the number of days in the numerator and the bags of scratch as a denominator.

And the last question is :

Is there a strategy to solving these kinds of questions or an easier way?

 

[PAllen]

That's what I tried to explain. I tried to give you a strategy not tied to some fixed equation. I'm not supposed to do the whole problem for you, only give hints. Perhaps it has been too long since such things were new to me, so I don't see where your difficulty lies.

Again:
<something> eats 10 bags of scratch in 20 days. You now have rate. But it is a rate for 5 chickens. What is the rate for 1 chicken? From that you should be able answer any further problem.

Beyond this, I don't know how to help without solving a problem for you.