Answer to September 19, 2005 Problem of the Week

Anne's birthday was this summer (2005).

James immediately pointed out that she was aging more quickly than he was.

Seventeen years ago, James was three times as old as she was then.

Four years ago, James was just two times as old as she was.

In the year 2027, James will be only one and one half times as old as she will be then.

1. What are the current ages of James and Anne?
2. Since Anne is aging so much more rapidly than James, how long before they will both be the same age?

Solution to the Problem:

(1) James is 56 and Anne is 30.
(2) They will never be the same age.

Let x = James' age in 2005.
Let y = Anne's age in 2005.

Then we can write two equations:
x - 17 = 3 (y - 17) <-- Seventeen years ago

x + 22 = 1.5 (y + 22) <-- Twenty-two years from now (in 2027)

Solving simultaneously, we obtain:
x - 17 = 3y - 51
2x + 44 = 3y + 66

So, x + 61 = 117

Therefore, x = 56, and y = 30.

Correctly solved by:

1. David & Judy Dixon	Bennettsville, South Carolina
2. John Funk	Ventura, California
3. Mike Singer	Winchester, Virginia
4. David McKinney	Winchester, Virginia
5. Jeffrey Gaither	University of Virginia Charlottesville, Virginia
6. Tristan Collins	Virginia Tech Blacksburg, Virginia
7. Avery Acuff	Columbus, Georgia
8. James Alarie	University of Michigan -- Flint Flint, Michigan
9. Malin Fredriksson	Tullängskolan, Örebro, Sweden
10. Nate Troup	Arlington, Virginia
11. Keith Mealy	Cincinnati, Ohio
12. Samantha H.	Washington Township HS, New Jersey
13. Maggie Morrison	Winchester, Virginia
14. Misty Carlisle	Cornell University Ithaca, New York
15. Erin Fennacy	Fresno, California
16. Rachel Pridgen	Columbus, Georgia
17. Richard Johnson	La Jolla, California
18. Ilir Dema	Toronto, Ontario, Canada
19. Ben Swartz	Stephens City, Virginia
20. Patrick McDuffee	Harrisonburg, Virginia
21. Rich Murray	Ridgetown, Ontario, Canada
22. Chris Rogers	Winchester, Virginia
23. Sharina Smith	Newport News, Virginia
24. Gusti Oggenfuss	Centre de Rencontre Montet (Broye), Switzerland
25. Charles Washington	Winchester, Virginia
26. Julianne Harris	Winchester, Virginia
27. Jessie Biggs	Winchester, Virginia
28. Mary Bailey Wickham	Columbus, Georgia
29. Anil Nataraj	Columbus, Georgia
30. Praveen Nandamuru	Columbus, Georgia
31. Olivia Quach	Harrisonburg, Virginia
32. Sagar Patel	Columbus, Georgia
33. Carter Galbraith	Columbus, Georgia
34. Cerena Uttal	Winchester, Virginia
35. John DeBergh	Winchester, Virginia
36. Angie Cutshaw	Williamsburg, Virginia
37. Walt Arrison	Philadelphia. Pennsylvania
38. Zaza Carlzon	Tullangsskolan, Örebro, Sweden
39. Wictoria Widén	Örebro, Sweden
40. Gabrielle Groth	Örebro, Sweden
41. Rickard Jansson	Tullängsskolan, Örebro, Sweden
42. Krille Jansson	Örebro, Sweden
43. Elizabeth Carlson	Winchester, Virginia

September 19, 2005 Problem of the Month

Correctly solved by:

September 19, 2005
Problem of the Month