Problem about a generous tourist who was left with an empty wallet

Cyril travels around India. During the day he wants to visit four temples and immediately proceeds to fulfill his plans. As soon as he enters any of the sanctuaries, the amount of his money immediately doubles (miracles!). At the exit, the tourist donates 100 rupees to each temple. When he leaves the last one, nothing remains in the wallet. How many rupees did Cyril have from the very beginning?

Solution 1

Let's start with the last temple.

After visiting the fourth sanctuary, Kirill has 0 rupees left. So, before that, he had (0 + 100) ÷ 2 = 50 rupees.

Before visiting the third temple, Cyril had (50 + 100) ÷ 2 = 75 rupees.

The tourist entered the second sanctuary with the amount (75 + 100) ÷ 2 = 87.5 rupees.

Before visiting the first temple, Cyril had (87.5 + 100) ÷ 2 = 93.75 rupees.

Answer: before the acquaintance with the sacred places in the traveler's wallet was 93.75 rupees.

Solution 2

Let Cyril had x rupees before visiting the temples.

The first temple. As soon as the tourist entered there, his money doubled to 2 x rupees. On the way out, he donated 100 rupees. So he has (2 x - 100) rupees left.

Second temple. Cyril entered the sanctuary, his money doubled to 2 × (2 x - 100), or (4 x - 200) rupees. On the way out, he donated 100 rupees. There are (4 x - 300) rupees left.

Third temple. Upon entering it, Cyril's money doubled to 2 × (4 x - 300), or (8 x - 600) rupees. Leaving the sanctuary, the traveler donated 100 rupees. He has (8 x - 700) rupees left.

The fourth temple. Cyril entered the temple, his money doubled to 2 × (8 x - 700), or (16 x - 1,400) rupees. On the way out, he donated 100 rupees. He has (16 x - 1,500) rupees left.

After the fourth temple, the tourist ran out of money. Hence, 16 x - 1,500 = 0; 16 x = 1,500; x = 93.75 rupees.

Answer: before visiting the temples, Cyril's wallet was 93.75 rupees.

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