Who Got Engaged to Whom?Date: 11/27/2001 at 19:23:17 From: Alina Mergelova Subject: Math mystery of the week Young people: Dorothy, Jean, Virginia, Bill, Jim, and Tom became engaged to one another (3 marriages to be). Who got engaged to whom? - Tom who is older than Jim, is Dorothy's brother. - Virginia is the oldest girl. - The total age of each couple is the same, although no two people are the same age. - Jim and Jean together are as old as Bill and Dorothy. Name the three pairs of engaged couples. Please help me! Thanks a lot. Date: 11/30/2001 at 17:56:36 From: Doctor Barney Subject: Re: Math mystery of the week Tom cannot marry Dorothy, because he's her brother. Tom cannot marry Virginia, either, because if he did, Jim (who is younger than Tom) would have to marry someone older than Virginia for their combined ages to be the same as Tom and Virginia's. But since neither of the other young women is older than Virginia, Tom cannot marry Virginia. Therefore, Tom must marry Jean. So who does Virginia marry? Suppose she marries Jim. IF Virginia marries Jim, Dorothy must marry Bill (he's all that's left). BUT Virginia and Jim's combined ages are more than Bill and Dorothy's combined ages, because Bill and Dorothy are together the same as Jim and Jean, and Virginia is older than Jean (she's the oldest girl). Therefore, Virginia cannot marry Jim. Virginia must marry Bill, and Dorothy will marry Jim. If you write their names on a piece of paper, draw lines between them, and make notes about their relationships, it helps. For example, I drew a line between Tom and Dorothy and wrote "brother/sister" on the line. Have Fun! - Doctor Barney, The Math Forum http://mathforum.org/dr.math/ |
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