Question

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