Answer to March 15, 2004 Problem

The Lottery Problem

 
Lucky Josh won $1,000,000 (a million dollars), split it up and gave it all to three male friends and their wives. The wives (together) received just $4,000 short of $400,000. Jane got $10,000 more than Catherine, and Marcy got that same amount more than Jane. John Green was given as much as his wife, Henry Brown got half again as much as his wife, and Tom Cobalt received twice as much as his wife.

What was the first name of each man's wife, and how much money did each of the six receive?

P.S. A few weeks ago, the winning ticket to the $230 million Mega Millions lottery was bought here in Stephens City, Virginia, where I live. The ticket is still unclaimed (No, I didn't purchase the ticket or you would already have received your check in the mail!).

 

Solution to the Problem:

Henry ($198,000) is married to Jane ($132,000).
Tom ($284,000) is married to Marcy ($142,000).
John ($122,000) is married to Catherine ($122,000)

We can determine the wives' amounts C+M+J=396 (thousand); J=C+10 :M=J+10
So C+(C+10)+(C+10+10)=396 or 3*C = 366 C=122, J=132, M=142.

The husbands need to add up to 604 (thousand).
Rather than just doing cases, let's observe that theoretically pairing any guy with any wife gives an even amount except Henry. The only way to take 1.5*(Wife amount) to get an even number is with Jane. So Henry must be married to Jane. Henry gets 198. So either 2*122 + 142 = 406 or 122 + 2* 142 =406. It is the latter. So Tom Cobalt ($284.000) is married to Marcy ($142,000), John Green($122,000) is married to Catherine ($122,000), and Henry Brown ($198,000) is married to Jane ($132,000).


Correctly solved by:

1. Walt Arrison Philadelphia, Pennsylvania
2. Jim Arrison Norristown, Pennsylvania
3. Akash Patel Columbus, Georgia
4. Richard Johnson La Jolla, California
5. David & Judy Dixon Bennettsville, South Carolina
6. Jason Storer Winchester, Virginia
7. Chris Maggiolo Harrisonburg, Virginia
8. Linda Liu Harrisonburg, Virginia
9. Elliot Kulakow Harrisonburg, Virginia
10. Lindsay Hawkins Columbus, Georgia
11. Monica Quach Harrisonburg, Virginia
12. Rachel Fovargue Harrisonburg, Virginia
13. Celeste Doerwaldt Winchester, Virginia
14. Ashleigh Rogers Winchester, Virginia
15. Jeffrey Gaither Winchester, Virginia
16. Kathryn Harris Winchester, Virginia
17. Franklin Harcourt Columbus, Georgia
18. Cody Dyke Harrisonburg, Virginia
19. Britney Ford Winchester, Virginia