Math problem bothering my mind

I'm not sure whether i'm posting in the right sub-forum but here it goes:

I should be able to do this but i cant remember or maybe this is harder than i think it is, i've been thinking about different solutions to this problem for about 1-2 hours now.

Let's imagine: I have 1 Copper bar,

with that 1 bar i'm able to do 5 copper sheets;
with 1 copper sheet i am able to do 2 copper studs;
with 2 copper sheets and 4 copper studs i'm able to do 1 copper ring.

What do i have to do to know how many sheets i have to turn into studs to make as many rings as to end up with a rate of 2(sheets) to 4(studs)
(to create as many rings without having any sheet or stud left in the end and not waste any resource)

Hope my explanation is clear and understandable

archgriffin said:

I'm not sure whether i'm posting in the right sub-forum but here it goes:

I should be able to do this but i cant remember or maybe this is harder than i think it is, i've been thinking about different solutions to this problem for about 1-2 hours now.

Let's imagine: I have 1 Copper bar,

with that 1 bar i'm able to do 5 copper sheets;
with 1 copper sheet i am able to do 2 copper studs;
with 2 copper sheets and 4 copper studs i'm able to do 1 copper ring.

Click to expand...

So one ring requires 2 sheet and 4 studs and each stud require 1/2 sheet: 2 sheets+ 4 studs= 2 sheets+ 4(1/2)= 4 sheets.

What do i have to do to know how many sheets i have to turn into studs to make as many rings as to end up with a rate of 2(sheets) to 4(studs)

Click to expand...

I don't know what you mean by "a rate of 2 sheets to 4. Since it requires 4 sheets to make one ring, two rings require 8 sheets, three rings require 12 sheets and four rings require 16 sheets.

(to create as many rings without having any sheet or stud left in the end and not waste any resource)

Hope my explanation is clear and understandable

Click to expand...

archgriffin said:

...to create as many rings without having any sheet or stud left in the end and not waste any resource...

Click to expand...

As you have posed the problem, you will have to have unused resource left over. As HallsofIvy pointed out, it will take the equivalent of 4 sheets to make one ring. That is given 4 sheets, take 2 of them and turn them into 4 studs. You will then have 2 sheets and 4 studs which you can use to make a ring. However, since a copper bar makes 5 sheets, you will have 1 sheet left over to either waste or do something else with.

If you had 4 bars, you could make 4 rings with 4 sheets left over. Use the 4 sheets to make another ring and you won't have any waste.