Distribution

[marquis]

It's been a while since I did something like this, and was wondering if I'm correct in this:

[this involves volume using the following metric system: liters, deciliters, centiliters, milliliters.]


1. Is this wrong or correct?
Let's say there are 300,000 liters of iron collected inside the city's center. The goal is to keep it steadily recycled after use and maintained when stored. All citizens have access
to the element in the form of credits.

How many days would it take for an entire population of 100,000 thousand to purchase 300,000 liters if said element was priced at 1 credit per liter?
-3 days. [3/1]

-How about:
-1 credit equals to 0.1 liters or 1 deciliter: 30 days [or 3/.1]
-or 1 credit is 1 centiliter: 300 days [or 3/0.1]
-or 1 credit is 1 milliliter: 3000 days [or 3/0.1]


2. Is this wrong or correct?
What if everyone receives 10 credits a week, how many weeks would it take for 100,000 people to consume all 300,000 liters of iron if 1 credit costs 1 milliliter?
-3000 divided by 10?
or
-10 x 52 - 3000?
-or some other algorithm I'm not seeing here?
-or could this be quicker/easier to solve using a higher understanding of mathematics/probability?


3. What would be the loophole or worse case scenario?
Or could one even exist in this case mathematically-speaking?

 

[ksdhart]

Let's say there are 300,000 liters of iron collected inside the city's center. The goal is to keep it steadily recycled after use and maintained when stored. All citizens have access
to the element in the form of credits.

How many days would it take for an entire population of 100,000 thousand to purchase 300,000 liters if said element was priced at 1 credit per liter?
-3 days. [3/1]

Without more information, there's no way to say if this is correct or not. The way the exercise is worded, the answer can be literally anything. How many credits does each person have available? Does everyone have the same amount of credits, or do some have more than others? At what rate do they purchase the iron with their credits? Etc.

2. Is this wrong or correct?
What if everyone receives 10 credits a week, how many weeks would it take for 100,000 people to consume all 300,000 liters of iron if 1 credit costs 1 milliliter?
-3000 divided by 10?
or
-10 x 52 - 3000?
-or some other algorithm I'm not seeing here?
-or could this be quicker/easier to solve using a higher understanding of mathematics/probability?

Okay, this part of the exercise has more information. If we assume that every person will spend all of their credits buying iron, then it's possible to find a solution. You know the cost per milliliter (mL), so what's the cost per liter (L)? Then how many credits would the entire 300,000 L cost? Each person has 10 credits per week, so how many total credits are available per week? Then how many weeks would it take to purchase the entire supply?

3. What would be the loophole or worse case scenario?
Or could one even exist in this case mathematically-speaking?

I'm sorry, but I don't understand what you're asking here.

 

[marquis]

Without more information, there's no way to say if this is correct or not. The way the exercise is worded, the answer can be literally anything. How many credits does each person have available? Does everyone have the same amount of credits, or do some have more than others? At what rate do they purchase the iron with their credits? Etc.

Sorry for the wording.
I was hoping to see if the math is correct. If 1L equals 1 credit, how many days would it take to consume 300,000L of iron if a 100,000 people purchased it every day with 1 credit a day?
3 days, correct?

Now how can we stretch this to last a bit longer?

What if I changed the 1 credit = x ratio to a smaller volume?
If 1mL equals 1 credit, how many days would it take for 100,000 people to consume 300,000L of iron if they purchase it every day with 1 credit a day?
3000 days, correct?

Okay, this part of the exercise has more information. If we assume that every person will spend all of their credits buying iron, then it's possible to find a solution. You know the cost per milliliter (mL), so what's the cost per liter (L)? Then how many credits would the entire 300,000 L cost? Each person has 10 credits per week, so how many total credits are available per week? Then how many weeks would it take to purchase the entire supply?

-300,000L = grand total amount of Iron.
-3 days to consume = if 1 credit equals 1L.

-If 1 credit equals 1mL = it would take 1000 credits to consume 1 liter.
-300,000L x 1000mL = 300,000,000mL.
-If 100,000 people each have 10 credits a week = together they make 1,000,000 total credits a week.
-300,000,000 divided by 1,000,000 = 300 weeks.
-300 weeks x 7 = 2,100 days.

It would take 2,100 days [or 300 weeks] for a population of 100,000 to consume 300,000 liters of iron IF they all spend 10 credits every week on the element, non-stop.

Correct?

I'm sorry, but I don't understand what you're asking here.

Oh, sorry about that. I was wondering if there was a short equation of some kind that could accurately utilize this problem in a different mathematical direction. Like probability, etc.

 

[Ishuda]

...Oh, sorry about that. I was wondering if there was a short equation of some kind that could accurately utilize this problem in a different mathematical direction. Like probability, etc.

As ksdhart pointed out, the problem needs to be defined before it can be solved. So as an example, let
T = the amount of iron collected
N = the number of people buying iron each day
C = cost of the iron
D = number of days an amount of T iron at cost C would last.
Then
D = T/(N*C)

Now you can put any kind of units you want on the cost and/or amount of iron. But if they are different, you must convert one to the other for the formula to work. Also the formula can be turned around to determine a cost for T iron to last D days, etc.