SOLUTION: a front is provisioned for 75 days . after 25 days a reinforcement of 500 men arrives and the food the lasts only 40 days. how many men were in the fort?

Question 688269: a front is provisioned for 75 days . after 25 days a reinforcement of 500 men arrives and the food the lasts only 40 days. how many men were in the fort?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
a front is provisioned for 75 days .
after 25 days a reinforcement of 500 men arrives and the food the lasts only 40 days. how many men were in the fort?
:
I assume they mean it will last 40 more days after the 25 days, a total of 65 days
:
Let m = original number of men
then a total of 75m man-days of provisions available
:
75m = 25m + 40(m+500)
75m = 25m + 40m + 20000
75m = 65m + 20000
75m - 65m = 20000
10m = 20000
m = 2000 men originally in the fort
;
:
:
See if this checks out:
2000*75 = 150000 man-days of provisions available
2000*25 = 50000 used in the 1st 25 days
2500*40 = 100000 using the last 40 days
total comes out right

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