Answer to the March 15, 2004 Problem of the Week

The Lottery Problem

• Home
• Meet Mr. P
• What's New
• Humor
• Lesson Plans
• Quotes
• Links
• Puzzles & Games
• Problem of the Month
• Math Facts
• Poetry
• Videos

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).