Question

Walking along Hadrian's Wall, a group of walkers encountered a man who claimed Discover a magical well. If a bag of money was put into the well, after counting to five, the well doubled the money on it. Stunned, the walkers asked him: “How much would it cost us to use the Good?" The man replied: "Every time you put a bag in the well and count to five, give me €148. Do you accept?" They accepted. The man put his bag in the well, counted until five and took it out. The money had doubled. The walkers took €148 from the bag, paid and He asked to repeat the operation. But the third time they did it, after paying €148 According to the man, the wallet no longer had any money in it! How is this possible?

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Answer to a math question Walking along Hadrian's Wall, a group of walkers encountered a man who claimed Discover a magical well. If a bag of money was put into the well, after counting to five, the well doubled the money on it. Stunned, the walkers asked him: “How much would it cost us to use the Good?" The man replied: "Every time you put a bag in the well and count to five, give me €148. Do you accept?" They accepted. The man put his bag in the well, counted until five and took it out. The money had doubled. The walkers took €148 from the bag, paid and He asked to repeat the operation. But the third time they did it, after paying €148 According to the man, the wallet no longer had any money in it! How is this possible?

$Expert avatar$

Miles

4.9

116 Answers

1. Let the initials be

M_0

2. After the first doubling, the money becomes

2M_0

3. After paying the fee, they have

2M_0 - 148

remaining
4. After the second doubling, they get

2(2M_0 - 148) = 4M_0 - 296

5. After paying the fee again, they have

4M_0 - 296 - 148 = 4M_0 - 444

6. After the third doubling, they get

2(4M_0 - 444) = 8M_0 - 888

7. After paying the fee for the last time, they have

8M_0 - 888 - 148 = 8M_0 - 1036 = 0

8. Solving for

M_0

8M_0 - 1036 = 0

8M_0 = 1036

M_0 = \frac{1036}{8}

M_0 = 129.50

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