Find amount of money

A magician had a magic bag that doubled the amount of moeny put into it. He agreed to allow a man to borrow te bag is the man gave the magician $16 after each doubling.Each time that the man used the bag, he put in all the money he had but after the fourth tim that he used the bag and paid the magician his money was comlpetly gone. With how much money did he start out with?

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Originally Posted by Godfather

A magician had a magic bag that doubled the amount of moeny put into it. He agreed to allow a man to borrow te bag is the man gave the magician $16 after each doubling.Each time that the man used the bag, he put in all the money he had but after the fourth tim that he used the bag and paid the magician his money was comlpetly gone. With how much money did he start out with?

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He starts with x amount of money.
After the first doubling, he has:
2x - 16

After the second doubling, he has:
2(2x - 16) - 16 = 4x - 32 - 16 = 4x - 48

After the third doubling, he has:
2(4x - 48) - 16 = 8x - 96 - 16 = 8x - 112

After the forth doubling, he has:
2(8x - 112) - 16 = 16x - 224 - 16 = 16x - 240 ... at which point, he had 0 dollars.

Solving this sitution, we have:
16x - 240 = 0
16x = 240
x = 15