A battalion 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 24.125 tons.