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 fathers’ 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.

My 5th grade students give the following answer:

Dad is 36, Mom is 23, the is adopted daugther is 6, she is older than the youngest who is celebrating her birthday, she is also 6.

They started with Dad's age, guessing the correct multiple of 6 the first try. Then they used clue 3 to determine Mom's age. With the number 23 known, they could compute the adopted daughter's age, and knowing she was 6 with a remainder of some days made her older, and not the birthday girl. Clue 4 verified adopted daughter's age, and clue 5 established age of younger bday girl.

They did not feel they had the clues to determine why it was dad's favorite day, but they guessed he had been in jail. They noticed his wife must have been young (17) when she first gave birth.

Posted by PEAK on 2004-11-18 23:34:43