Question

1200 soldiers in a fort had enough food for 28 days. After 4 days, some soilders were sent to another fort and thus, the food lasted for 38 more days. How many soilders left the fort?

Answer 1

let the food needed each day per soldier be x units
total food available = 1200(28)x = 33600x
after 4 days, 6/7 of the amount would be left
or (6/7)(1200)(28)x
= 28800x

let the number of soldiers who left be n
so (1200 - n)(x)(38) = 28800x
(1200-n)(38) = 28800
45600 - 38n = 28800
-38n = -16800
n = 442.1

442 soldiers left the fort

check:
suppose each soldier needed 2 kg per day
total needed for the 28 days = 2(1200)(28) or 67200 kg
food used in 4 days = 4(2)(1200) = 9600 kg

So amount of food left = 67200-9600= 57600 kg

442 soldiers left, so
remaining soldiers = 758
amount used by those 758 for 38 days
= 38(758)(2)
= 57608 , close enough