"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?
The Big Hen Weighs 16 pounds
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
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
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.
jajajaja, I think i need some sugar, or maybe i am just not awake enogh jajajaja, three equations three variables jajajaja:
rice= 18,5
here its the cuadratic expression:
10Price(squared)-169Price -296= 0 –>
Pp=296/18,5–>16 I think I must quit Splenda and go back to sugar jajajaja
I’m probably way off, but I have it weighing about 16 lbs…
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……
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
16 lbs.
That’s a big hen. I guess the picture represents what the hen would look like.
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.
These are so much easier when the answers are posted.