A bottle and drinking glass on the left side of a scale balance with a jug on the right side.
The bottle alone balances the drinking glass and a plate.
Three of these plates balance 2 of the jugs.

How many of the glasses will balance a bottle?

 

Solution to the Problem:

Let B represent a bottle, G a drinking glass, J a jug and P a plate.
Let "=" represent being in balance.
We are given the following:

BG = J

B = GP

PPP = JJ

Given: BG = J, add J to both sides to get: JBG = JJ

Then: PPP = JBG

Add 3 G's to both sides and replace J with BG to get: GPGPGP = GGGBGBG

Now replace each GP with B to get: BBB = GGGGGBB

Lastly, remove two B's from both sides to get: B = GGGGG

Therefore five drinking glasses balance one bottle.

Here is a more algebraic approach sent in by Ann Norman:
let b stand for bottle, g stand for glass,and j stand for jug.
b+g=j
b=g+p
3p=2j

b=j-g
j-g=g+p
j=2g+p
3p=2(2g+p)
3p=4g+2p
p=4g
p=b-g
b-g=4g
b=5g

Correctly solved by:

1. Ann Norman Columbus, Georgia
2. Van Pham Harrisonburg, Virginia
3. Larry Schwartz Trumbull, Connecticut
4. John Funk Ventura, California
5. Tarpley Ashworth Harrisonburg, Virginia
6. Cameron Burkholder Winchester, Virginia
7. Jim Arrison Norristown, Pennsylvania
8. Andrea Eberhard ----------
9. António Baptista Lisboa, Portugal
10. Charles Washington Winchester, Virginia
11. Molly Simkins Columbus, Georgia
12. Ben Swartz Winchester, Virginia
13. Thomas Woodward Columbus, Georgia
14. Tom Robb Winchester, Virginia
15. Weimers Winners Lordstown, Ohio
16. James Alarie University of Michigan -- Flint,
Flint, Michigan
17. Angelo Leone Middletown, Connecticut
18. Rich Murray Ridgetown, Ontario, Canada
19. Cougar5447 Columbus, Georgia
20. Kevin Jacobson Columbus, Georgia
21. Sarah Watterson Middletown, Connecticut
22. Sheila Shah Arlington, Virginia
23. Emily Auerbach Columbus, Georgia
24. Amanda Auerbach Columbus, Georgia
25. Jeffrey Gaither Winchester, Virginia
26. Irene Mathieu Winchester, Virginia
27. Tristan Collins Winchester, Virginia
28. David & Judy Dixon Bennettsville, South Carolina
29. Chelsea Smith Columbus, Georgia
30. Alex McIntire Columbus, Georgia
31. Viktor Logrell, Jonathan Jansson, Bahadér Güngör, Ako Saleh Tullängensskolan, Örebro, Sweden
32. Rob Adams Winchester, Virginia
33. Gilbert Melanson Sierra Vista, Arizona
34. David Amos Winchester, Virginia
35. Jason LaRusso Winchester, Virginia
36. William Proffitt Winchester, Virginia
37. Mike Hudson Winchester, Virginia
38. Wajih Ansari Harrisonburg, Virginia
39. Okechi "pithy" Egekwu Harrisonburg, Virginia
40. Arin Smith Winchester, Virginia
41. Chris Hernley Winchester, Virginia
42. Kelly Johnson Columbus, Georgia
43. James Simmons Harrisonburg, Virginia
44. John Harcourt Columbus, Georgia
45. Arsalan Heydarian Harrisonburg, Virginia