Word problem - number of provisions

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mameha

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Sep 29, 2007
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I'm having difficulty translating this problem into the appropriate equations:

A fort has provisions for 60 days. If after 15 days 500 men strengthen them and the food lasts 40 days longer, how many men are in the fort?

So if

M = # of men
P = # of provisions
D = # of days

Then, the number of provisions would have to equal P = MD right?

So the original condition is P = M(60)

After 15 days there will be P = M(45), and after the 500 men join the original group, P = (M + 500)(45)...it's the "40 days longer" that's tripping me up.

Any help would be greatly appreciated!
 
mameha said:
A fort has provisions for 60 days. If after 15 days 500 men strengthen them and the food lasts 40 days longer, how many men are in the fort?
Click to expand...
I don't see how this question makes any sense! :shock:

You'd had some number of men, and food for them for sixty days. Then you get five hundred more men (but no more food), and somehow the same food will now last an additional forty days...? How is that possible? :oops:

Eliz.
 
4,000 men

provisions[P] for x men for 60 days
15 days later we have 500+x men
provisions left will last the 500+x men 40 days

each man consumes c lbs per day
x men consume xc lbs per day
number of days provisions P will last is 60 days
the P/[xc] = 60

let P' be the provisions after 15 days
P'/[c[x+500]]=40
but P'=P-15xc
substitute
[P-15xc] / [[c[x+500]=40
but P =60xc
[60xc-15xc] / [c[x+500]] = 40
factor out c and cross multiply
45x=40[x+500]
45x=40x+20,000
5x=20,000
x=4,000 answer

as a check assume you started with 4,000 men and each ate 5 lbs per day
see if after 15 days the remaining food would last 40 days
Arthur
 
I suppose they mean "40 more days" after those 15 days.

Now instead of lasting total 60 days - it will last total (15+40 = )55 days.

After that the questioneer should be hung by his toes from the rafter of the fort....
 
subotash-
Beautiful!
I had to solve it by a very unelegant manner.

Of course:
x+500 men can last for 40 days on provisions left after 15 days
x men can last for 45 days on provisions left after 15 days

YOUR INSIGHT IS GREAT. I should have seen that approach
Arthur
 
Subhotosh Khan said:
I suppose they mean "40 more days" after those 15 days.

Now instead of lasting total 60 days - it will last total (15+40 = )55 days.

After that the questioneer should be hung by his toes from the rafter of the fort....
Click to expand...



:lol:

Thank you all very much for your explanations...that question was racking my brain (especially with how it was worded!)
 
your welcome. I also learned that I should look for more elegant solutions rather than brute force.
Arthur
 
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