Abattalion of 520 soldiers goes through 16,380 pounds of rations in 3 weeks. if 780 more soldiers join the battalion, how many tons (1 ton 2,000 pounds) of rations would the battalion now need to sustain its soldiers for 5 weeks?

They would need 34.125 tons of rations.

In order to find this, we first need to see how many pounds of rations a single soldier eats in a week. To do this, we take the total eaten in 3 weeks and divide by 3. Then we divide by the number of soldiers.

16,380/3 weeks= 5460 lbs per week

5460/520 soldiers = 10.5 lbs per soldier per week

Now we look to see how many soldiers we will have in total after adding. There are 520 to start and we add 780 to get 1300 total. Next we multiply that by the total per soldier per week.

10.5lbs per soldier per week * 1300 soldiers = 13,650lbs per week

Then we have to multiply by the 5 weeks that battalion will be there.

13,650lbs * 5 weeks = 68,250lbs of rations or 34.125 tons.

The amount of rations required is assumed to be proportional to both time and the number of soldiers.

The number of soldiers has increased from 520 to (520+780=) 1300. This is a factor of 1300/520 = 2.5 times the original number.

The length of time has increased from 3 weeks to 5 weeks, so is 5/3 the original length of time.

Then the amount of rations required will be (2.5)(5/3)(16,380 lb) = 68,250 lb. This number is 34.125 times 2000 lb.

34 1/8 tons of rations will be needed now to sustain the soldiers for 5 weeks.