Dinner Party
DualAspect takes a break from his hang-gliding, sky-diving, and lion taming to host a dinner for several of his Puzzlarian neighbors. He decides to prepare a turkey for the get together, and visits the local butcher to purchase a bird.
As he enters the butcher shop, he sees a puzzle buddy Chris. He listens as the butcher explains pricing.
"The little birds sell for two cents a pound more than the big birds. As you can see, I have pulled two turkeys from cold storage ... together they weigh twenty pounds," said the butcher.
Chris offers to go by the Puzzlarian ABC and get beverages for the evening. Dual buys both birds ... paying 82¢ for the small bird and $2.96 for the larger.
How much did each gobbler weigh?
As he enters the butcher shop, he sees a puzzle buddy Chris. He listens as the butcher explains pricing.
"The little birds sell for two cents a pound more than the big birds. As you can see, I have pulled two turkeys from cold storage ... together they weigh twenty pounds," said the butcher.
Chris offers to go by the Puzzlarian ABC and get beverages for the evening. Dual buys both birds ... paying 82¢ for the small bird and $2.96 for the larger.
How much did each gobbler weigh?
posted by Zaux at
9:42 AM
11 Comments:
"How much did each gobbler weigh?"
Just to clarify Zaux....are you asking for the weight of each turkey, or of Chris and myself after eating them?
:-)
If it's the turkeys you're after then I get small = 4.72lb, large = 15.28lb.
Cost of each: small = 17.37c / lb, large = 19.37c / lb.
These seem to be accurate to 2 decimal places but not absolutely precise, but then how accurately can you weigh a turkey?
No fancy method unfortunately, just brute force, I'm sure Chris (or someone else) can show us some technical maths to get there and will probably get the accuracy down to a few more decimal places.
Ooops, just realised I got that the wrong way round, I've calculated for the small ones to be 2c cheaper.
I'll have another go.
Oh, that's a bit easier.
Weight - Small: 4lb, Large: 16lb
Cost - Small: 20.5c / lb, Large: 18.5c /lb.
Dual ...
that is correct
did you notice I changed your leisure activites? ... although, there's nothing wrong with grabbing the Strat and whipping out some cool blues
Help! ....
Dual solved it by brute force ...
I attempted an algebraic solution and failed ... please ...someone show it algebraically.
Yeah thanks Zaux, I think it was the extreme sports adrenaline rush that caused me to misread the question first off!
I'd be interested in the mathematical solution too. I couldn't see the way through it with so many unknown variables.
Your wishes are my command:
Let C be the cost per lb of the larger bird. Let S and L be the
weights of the smaller and larger birds. We are given:
1) S+L = 20, 2) 82 = S(C+2), 3) 296 = LC
Subst 1) int 2) => 4) 82 = (20-L)(C+2), subst 3) into 4) =>
82 = (20 - 296/C)(C+2), *C => 82C = (20C - 296)(C+2)
=> 82C = 20C² - (296-40)C + 596
=> 20C² - 338C + 596 = 0
=> C = (338 +/- Sqrt(338² + 4*20*596))/40
=> C = (338 +/- 402)/40
As DualAspect pays rather than receives money
=> C = 740/40 = 18.5
Subst into 2) => 82 = 20.5*S => S = 4
Subst for C into 3) => L = 296/18.5 = 16
This post has been removed by the author.
Chris ...
thanks ... I need my butt kicked ... I started with the same three equations you set up, and then apparently made a mistake somewhere along the way.
After about a hundred years of not using much math, it is slowly returning. I enjoy analyzing your approaches ... you are helping me to get better.
Hi Zaux. Thanks for the comment. Keeping my hand in is a large part of why I come to this site. I haven't had to use maths in real-life for a very long time. Also, it's very easy to get into a muddle with these problems; one small slip blows the whole deal.
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