The Gambler Who Never Win ( Solving Problem From The Back)

Algebra Level 3

A gambler walks through three casinos. Upon entering, he paid $10.00. He won and doubled all his money in a card game. He again paid $10.00 as he walked out of the casino. In the second casino, he paid $10.00 as he entered, doubled his money upon winning. He paid again $10.00 as he left. He did the same in the third casino but upon leaving, he had nothing left. How much was his original amount of money?

Details

If your answer is $A => Submit A (eg. $10.00, submit 10.00)

This question is not my original :D

notes

Parallel Question

Parallel Question 2


The answer is 26.25.

Paul Ryan Longhas by Paul Ryan Longhas , 24, Philippines

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2 solutions

David Holcer
Feb 21, 2015

My method was as follows:

  1. I began by setting the original amount of money to n dollars.
  2. Upon entering the First casino he pays 10 so his total is now n -10
  3. He wins and doubles his total. Because he was at n -10 , he is now at 2 n -20
  4. Once again, he pays 10 dollars, and he is at 2 n -30
  5. He now enters the Second casino and pays his 10 dollars, bringing him to 2 n -40
  6. He doubles his money, bringing him to 4 n -80
  7. He pays the 10 dollars as he exits and now has 4 n -90
  8. He enters the Third casino, and pays the entrance fee, bringing him to 4 n -100 dollars.
  9. He once again doubles his money, and now has 8 n -200 dollars.
  10. Finally, he pays his 10 dollars as he exits and now has 8 n -210 dollars.
  11. We know that he comes out with no money left, so we can create the equation 8 n -210=0 which results in n being 26.25 \boxed{26.25} dollars.
2 Helpful 0 Interesting 0 Brilliant 0 Confused
Paul Ryan Longhas
Feb 20, 2015

3rd Casino

10 2 + 10 = 5 + 10 = $ 15 \frac{10}{2} + 10 = 5+10 = \$15 money left before entering third casino.

2nd Casino

15 + 10 ( e x i t ) = 25 15 + 10(exit) = 25 = > 25 2 + 10 = 12.50 + 10 = $ 22.50 => \frac{25}{2} + 10 = 12.50 + 10 = \$22.50 , money left before the entering 2nd casino

1st Casino

22.50 + 10 = 32.50 = > 32.50 2 + 10 = $ 26.25 22.50 + 10 = 32.50 => \frac{32.50}{2} +10 = \$26.25 the original amount of money

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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