School-Safe Puzzle Games

Marketplace Hens Puzzle

"These are all the hens we have left", said the butcher to the 3 women who were shopping in the market. "Together they weigh 20 pounds, and the little bird sells for 2 cents a pound more than the big bird."

Mrs. Davis bought the little one for 82 cents, and Mrs. Miller paid 2 dollars and 96 cents for the big hen.

Can you tell Mrs. Johnson how many pounds the big hen weighs?

11 Comments to “Marketplace Hens Puzzle”


  1. lookingforchallenge | Profile

    The Big Hen Weighs 16 pounds


  2. virtualetters | Profile

    This one seems really easy but I’m stumped for a simple way of solving it without estimating and refining. I could bring in the linear algebra but I’m looking for a “finger math” method.


    The big hen weighs 16 pounds, assuming half penny prices were in existence


  3. suineg | PUZZLE MASTER | Profile

    I think is 16 pounds. Explanation:


    Price( WHeavy)= 296 cents
    (Price+2)(WThin)= 82 cents
    WHeavy + WThin= 20 pounds

    If all the hens cost the same this will result:
    Price*WHeavy=296
    Price*Wthin=82
    so: WHeavy/Wthin=296/82–> 3,60 so the heavy would be almost be 4 times heavier than the thin one, so in the original problems this relationship increased:


    so the weight relationship its at least 4
    and add up 20 :
    substitute in the original equations:
    4;16 4 in 20,5 cents 16 in 18,5 cents


    I could not do it by deduction only by induction, so i found it hard, also I assume that there were only two hens, but maybe there could be more. WoW


  4. cjsmed | Profile

    The big hen weighs 16 lbs (at 18.5 cents/lb). Therefore, the small hen weighs 4 lbs (at 20.5 cents/lb or 2 cents more per pound than the big bird).


    It doesn’t say there are only 2 birds, so you could calculate it for 3 birds (or more) as well.


  5. suineg | PUZZLE MASTER | Profile

    jajajaja, I think i need some sugar, or maybe i am just not awake enogh jajajaja, three equations three variables jajajaja:
    here its the cuadratic expression:
    10Price(squared)-169Price -296= 0 –>;Price= 18,5
    Pp=296/18,5–>16 I think I must quit Splenda and go back to sugar jajajaja


  6. jason | Profile

    I’m probably way off, but I have it weighing about 16 lbs…


  7. jason | Profile

    honestly though, I am not sure how many hens are there…..it isnt specified. So my answer is NO, i cannot tell her anything……but thats just me……


  8. Shawn | PUZZLE GRANDMASTER | Profile

    4 equations, 4 unknowns


    WL=weight of little hen
    WB=weight of big hen


    CL=cost/pound of little hen
    CB=cost/pound of big hen


    WL+WY=20
    CL=CB+.02
    WL*CL=.82
    WB*CB=2.96


    Big hen weighs 16 pounds


    Little hen weighs 4 pounds
    Little hen costs $.205/pound
    big hen costs $.185/pound


  9. carlhazlewood | Profile

    16 lbs.


    That’s a big hen. I guess the picture represents what the hen would look like.


  10. RK | Profile

    I thought this was very challenging.


    the answer we were looking for is: Big Hen= 16 pounds (Although as Jason & CJmed note, it doesn’t say there are only 2 birds)


    Shawn, and Suineg, provide some very helpful explanations.


  11. TwisterMc | Profile

    These are so much easier when the answers are posted. :)


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