An army of ants was migrating. The ants moved 120 grams less than half of their food on their first trip. On their second trip, they managed to move 100 g more than half of the remaining amount of food. They moved 480 g of food on their third trip. 280 g of food was still unmoved. How much food did the army of ants have at first?

Answer 1

Just take it deliberately and slowly.

amount at start ---- x g
amount moved on first day: x/2 -120
amount left at end of first day = x - (x/2-120) = x/2 + 120

second day
amount moved = (1/2)(x/2 + 120) + 100
= x/4 + 160
amount left at end of 2nd day = (x/2 + 120) - (x/4 + 160) = x/4 - 40

amount left after 480 g was moved on 3rd day
= x/4 - 40 - 480 = x/4 - 520

but this equals 280
x/4 - 520 = 280
x/4 = 800
x = 3200 g