Proportions: food for 300 men for 90 days. After 20 days, 50 men left. How long...?

[Uzayr]

A fort had provisions for 300 men for 90 days. After 20 days, 50 men left the fort. How long would the food last at the same rate.

So men is inversely proportional to days

so with 300 and 90 the constant is 27000

if you use the fact that after 20 days 50 men left you can use 250 men and you get 108 days is that correct?

 

[Deleted member 4993]

A fort had provisions for 300 men for 90 days. After 20 days, 50 men left the fort. How long would the food last at the same rate.

So men is inversely proportional to days

so with 300 and 90 the constant is 27000

if you use the fact that after 20 days 50 men left you can use 250 men and you get 108 days is that correct?

After 20 days, 70 days left and (300*70 = ) 21000 man-days of food left for 250 men.

That will last them (21000/250 =) 84 days.

 

[Uzayr]

But since the question says at the same rate the 300 men and the 250 men eat the food at the same rate. So is it not just 300 times 90 / 70 giving you 108 days?

 

[stapel]

A fort had provisions for 300 men for 90 days. After 20 days, 50 men left the fort. How long would the food last at the same rate?

I would assume that "the same rate" means "the same per-person, per-day rate of consumption". Otherwise, you're assuming that the rate is "per day, regardless of the number of persons", which means that it doesn't matter that fifty guys have left.

So men is inversely proportional to days

How are you arriving at this? Since the number of men did not decrease consistently with the increase in the number of days, I see no reason to conclude an inverse relation.

so with 300 and 90 the constant is 27000

What "constant"? (It almost sounds like you're trying to set up some sort of variation equation, but that requires algebra and you posted this to "Arithmetic", so a variation equation, with its constant of variation, makes little sense.)

Please reply explaining your reasoning and methodology. For instance, being in a before-pre-algebra class, you can only use basic arithmetic operations:

You figured that there were means for three hundred people each, for ninety days; in other words, after multiplying, you found that there were 27,000 days' worth of food in storage. In twenty days, how many of those days of meals had been eaten by the three hundred guys? (Hint: Multiply.) How many days of meals were left? (Hint: Subtract.) After that twentieth day, how many guys were left? (Hint: Subtract.) Over how many days can those remaining guys split the remaining days worth of meals? (Hint: Divide.)

Where are you getting confused? Thank you!

 

[Uzayr]

I would assume that "the same rate" means "the same per-person, per-day rate of consumption". Otherwise, you're assuming that the rate is "per day, regardless of the number of persons", which means that it doesn't matter that fifty guys have left.


How are you arriving at this? Since the number of men did not decrease consistently with the increase in the number of days, I see no reason to conclude an inverse relation.


What "constant"? (It almost sounds like you're trying to set up some sort of variation equation, but that requires algebra and you posted this to "Arithmetic", so a variation equation, with its constant of variation, makes little sense.)

Please reply explaining your reasoning and methodology. For instance, being in a before-pre-algebra class, you can only use basic arithmetic operations:

You figured that there were means for three hundred people each, for ninety days; in other words, after multiplying, you found that there were 27,000 days' worth of food in storage. In twenty days, how many of those days of meals had been eaten by the three hundred guys? (Hint: Multiply.) How many days of meals were left? (Hint: Subtract.) After that twentieth day, how many guys were left? (Hint: Subtract.) Over how many days can those remaining guys split the remaining days worth of meals? (Hint: Divide.)

Where are you getting confused? Thank you!

I think its a much simpler sum then creating equations its just the language that is confusing. So I think 84 or 108 would be fine

 

[stapel]

I think 84 or 108 would be fine

No; this exercise will have only one valid answer.

Are you assuming that the number of men matters? Or not? If not, why not?

Thank you!

 

[Uzayr]

No; this exercise will have only one valid answer.

Are you assuming that the number of men matters? Or not? If not, why not?

Thank you!

The rate at which the eat is important in this question. They eat at the same rate as 300. So 90 times 300 = 27000 is the rate the 300 men eat. 250 men eat at that rate so 27000/250 = 108 days

 

[Deleted member 4993]

The rate at which the eat is important in this question. They eat at the same rate as 300. So 90 times 300 = 27000 is the rate the 300 men eat. 250 men eat at that rate so 27000/250 = 108 days

No.

In that calculation, you are assuming no food were consumed for the first 20 days.

You need to calculate the amount of food consumed in the first 20 days (= 27000 * 20/90) then subtract that mount from 27000 to know the amount of food left. Now divide by 250 to get the remaining days.

 

[Uzayr]

Yes thanks I see it now

 

[Vanice]

A fort had provisions for 300 men for 90 days. After 20 days, 50 men left the fort. How long would the food last at the same rate.

So men is inversely proportional to days

so with 300 and 90 the constant is 27000

if you use the fact that after 20 days 50 men left you can use 250 men and you get 108 days is that correct?

Let's just say that the fort had 27000 pieces of meat. Each men will eat a meat a day. There will be no meat in the 90th day.

In 20 days 6,000 pieces of meat is eaten. 21,000 of meat had left. 21,000 divided by 250 is 84. So 104 days have passed there is no meat in the fort left

 

[stapel]

Let's just say that the fort had 27000 pieces of meat. Each men will eat a meat a day. There will be no meat in the 90th day.

In 20 days 6,000 pieces of meat is eaten.

How did you arrive at "27,000" and "6,000"? What were your steps? What was your reasoning?

Please be complete. Thank you!

 

[Vanice]

Agree with Vanice.
27000 is simply another way to represent man-days.
(see Subhotosh's post).

(27000 - 300*20) / (300 - 50) = 84

Hey Vanice, are you from Venice?

Nope. I was confused how do you get at 108 anyway. I understand you didnt add 20 at 84