SOLUTION: A fort has enough provisions to feed everyone in it for 90 days. After 20 days, 600 more soldiers arrive as reinforcements, and the food only lasts 50 days longer. How many people

Question 1113725: A fort has enough provisions to feed everyone in it for 90 days. After 20 days, 600 more soldiers arrive as reinforcements, and the food only lasts 50 days longer. How many people were in the fort originally?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
.

n*(90-20) = (n+600)*50 ( <<<---=== it is what the condition says . . . ) 70n = 50n + 3000 20n = 3000 n = = 1500. Answer. 1500 people were in the fort originally.

Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

When the new soldiers arrive, the food that was going to last another 70 days is now going to last only another 50 days.

Since the ratio of the numbers of days the food is going to last is 70:50 = 7:5, the ratio of the number of soldiers before and after the arrival of the reinforcements must be 5:7. So if x is the number of soldiers at the fort initially,

There were 1500 soldiers at the fort initially.
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