I need help on a tricky problem

[sashary]

I have tryed to figure it out but I didn't get an aswer :?


you are playing a game that uses points to buy items you want to buy something that costs 2400 points but you don't have that many points so you make a deal with the person selling the item "I'll buy your item but only if you let me borrow the same amout of points that I have right now" the person agrees and you go to a different person you make the same deal with that person then with 2 other people you buy an item that costs 2400 from each of them How many points did you start of with?

I hope someone can give me an asnwer

 

[Denis]

Starts with x

1: gets x, spends 2400: 2x - 2400

2: gets 2x - 2400, spends 2400: 4x - 7200

3: gets 4x - 7200, spends 2400: 8x - 16800

4: gets 8x - 16800, spends 2400: 16x - 36000

So 16x - 36000 = 0
16x = 36000
x = 2250

Proof:
starts with 2250
1: 2250 + 2250 - 2400 = 2100
2: 2100 + 2100 - 2400 = 1800
3: 1800 + 1800 - 2400 = 1200
4: 1200 + 1200 - 2400 = 0