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The Census Puzzle

September26

problemDelight yourself in some mathematical detective work to see if you can figure this problem out!

A member of a census organization is going door-to-door collecting information. He comes to a house where a woman answers the door. After introducing himself, he asks her how many adults live in the house. “Just me,” she replies, as the screaming and yelling of children pierce through from the living room. “I’m guessing you have children,” he astutely asserts, “how many?” “I have three, and they’re about to drive me out of my mind. How many of them do you want?” She asks back. “Um, ma’am, if you’ll simply allow ME to ask the questions,” he rudely replies. “Now if you could please tell me the ages of your three children, I’ll be on my way.” Feeling offended, the woman becomes irritated and less cooperative. “Absolutely NOT,” she retorts. “You’ll have to work at it now Mr. Census man. Here’s a clue. If you multiply all their ages together, you get thirty-six.” She then slams the door in her face.

censusquThe census man pulls out his calculator from his pocket and punches a few numbers, then knocks on the door again. When the woman answers the door this time, she is even more irate as the sounds of obstreperous children spill out of some hidden room in the house. “Sorry to bother you again, ma’am, but could you please offer me one more hint as to your children’s ages?┬áThe woman replies, “If it’ll get you off my doorstep, you should know that the sum of their ages equals the address number on the house across the street.” Then, BAM!, she slammed the door shut.

Determined to get this information, the census taker runs across the street and peers at the number on its mailbox. He again pulls out his calculator, punches a few keys, then scratches his head a bit. With a determined temerity, he knocks on the woman’s door once again. “I’m so sorry to bother you again, but I need to have just one last clue and I’ll be our of your hair for good.” (Screams emanated from inside the house) “You’re just like my oldest,” she said “unrelenting!” Then she retreated back into the house and was gone.

Now the census man may not be suave, but he’s no dummy. From her last, subtle clue regarding her child’s temperament, he is able to discern the ages of each of her three children. Can YOU figure their ages out? (Answer here)

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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