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The Fair (Posted on 2004-11-08) Difficulty: 3 of 5
A couple is taking their two daughters to a local fair. They are celebrating a birthday of one of the girls. It also marks the fathersí favorite day of the year because it reminds him how lucky he is to not be barred from such festivities. Use the clues below to determine the ages each family member; which daughter is adopted; which daughter is the birthday girl; what is the difference in age of the two girls.

Bonus question: Why is it the fathers favorite day?

1. Dad is six times older than his youngest daughter.
2. The adopted daughters' age in days is 100 times her adopted mother's age in years.
3. In three years the dad will be exactly three times the difference in age between him and his younger wife.
4. The age of the two parents together is one less than ten times the eldest daughter's age.
5. The combined age of all four family members in whole years is seventy-one.

Note: Ages are to be taken in years unless otherwise stated and assume there is no leap year.

  Submitted by Jeremy Trenary    
Rating: 3.6667 (6 votes)
Solution: (Hide)
Solution:
There are 4 parties Mother (M), Dad (D), Eldest Daughter (ED), and Youngest Daughter (YD).

Clue 1: 6YD=D
Clue 3: D+3=3(D-M) solving for M=2/3D-1
Clue 4: M+D+1=10ED solving for ED= 1/10M + 1/10D +1/10
Clue 5: M+D+ED+YD=71
Now substitute so that all terms are in YD
D=6YD
M=2/3(6YD)-1 or M= 4YD-1
ED=1/10(4YD-1) + 1/10(6YD) + 1/10 or ED=YD
Plug these into the formula supplied in clue 5
4YD-1 + 6YD +YD + YD=71 solving for YD=6
Since YD=6, ED=6
D=6YD or 6(6) or 36
M= 4(YD)-1 or 4(6)-1 or 23
Clue 2: 100M=2300 days or 6.301 years old the eldest daughter must be adopted and the youngest daughter must be the birthday girl.
The birthday girl is 6 years old today or 365(6)=2190 days old. The eldest girl is 110 days older than the youngest daughter.

Bonus: The mother is 23 years old now which means she was 16/17 when she became pregnant. The father at that time would be 29/30 years old. He is lucky he is not in prison for statutory rape.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Bonus answerOwen Lorion2006-10-27 09:27:05
re: Bonus answer?LetheAren2005-05-27 18:23:47
not sure about this one...LetheAren2005-05-27 18:04:36
BonusJen2005-01-27 16:15:54
solutionwhome?2005-01-23 18:16:46
this has to be itlashondera tarrance2005-01-10 07:41:24
woa tuffAlbert2005-01-06 01:09:22
Bonus answer?JP2004-12-10 19:24:07
re(3): Solutionjmnw2004-11-30 00:19:47
re(2): SolutionMichael2004-11-28 00:23:15
re: Solutionbill2004-11-27 18:19:18
SolutionSolutionMichael2004-11-27 04:46:26
SolutionFull solution - Rather longUrza2004-11-21 16:27:31
PEAK GT5PEAK2004-11-18 23:34:43
re: Answer + Solution/Explanationandrew2004-11-14 05:28:19
re(2): Solution?Trevor2004-11-10 12:28:19
SolutionAnswer + Solution/Explanationnikki2004-11-08 13:40:01
re: Solution?Charlie2004-11-08 13:02:23
Solution?Ruth2004-11-08 11:39:23
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