All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Who began with 50 cents? (Posted on 2017-09-06) Difficulty: 3 of 5
Three bets were made:

(1) First, A won from B as much as A had originally.
(2) Second, B won from C as much as B then had left.
(3) Finally, C won from A as much as C then had left.

The three players ended up with equal amounts of money.

Who began with 50 cents?

No Solution Yet Submitted by Jer    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution | Comment 2 of 3 |
A started with amount a.
B started with amount b.
C started with amount c.

                 A          B            C
After 1st bet:   2*a        b-a          c
After 2nd bet:   2*a        2*(b-a)      c+a-b
After 3rd bet:   a-c+b      2*(b-a)      2*(c+a-b)


a-c+b = 2*b - 2*a
3*a - b = c            (i)

a-c+b = 2*c+2*a-2*b
3*b - a = 3*c          (ii)


6*b - 10*a = 0         (ii) - 3 * (i)

3*b = 5*a

b     a     c
5     3     4
10    6     8
15    9     12
20    12    16
...
50    30    40

B started with 50 cents, as 50 is not divisible by 3 or by 4.


  Posted by Charlie on 2017-09-06 13:13:58
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information