## 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?

lookingforchallenge| Profile January 14th, 2008 - 6:09 amThe Big Hen Weighs 16 pounds

virtualetters| Profile January 14th, 2008 - 8:21 amThis 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

suineg| PUZZLE MASTER | Profile January 14th, 2008 - 10:35 amI 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

cjsmed| Profile January 14th, 2008 - 10:47 amThe 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.

suineg| PUZZLE MASTER | Profile January 14th, 2008 - 11:29 amjajajaja, 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 –>rice= 18,5

Pp=296/18,5–>16 I think I must quit Splenda and go back to sugar jajajaja

jason| Profile January 14th, 2008 - 1:51 pmI’m probably way off, but I have it weighing about 16 lbs…

jason| Profile January 14th, 2008 - 2:08 pmhonestly 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……

Shawn| PUZZLE GRANDMASTER | Profile January 14th, 2008 - 3:07 pm4 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

carlhazlewood| Profile January 14th, 2008 - 3:52 pm16 lbs.

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

RK| Profile January 15th, 2008 - 9:27 pmI 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.

TwisterMc| Profile January 16th, 2008 - 12:47 pmThese are so much easier when the answers are posted.