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RE: The Chicken Game

animeglider — Sun, 23 Dec 2007 07:56:30 GMT

There are 2 important equations that we have in this problem:

Chickens = C
Hens = H
Roosters = R

C + H + R = 100 (Total Chickens + Total Hens + Total Roosters = 100)
.5*C + 1*H + 5*R = 100 (Cost of Chickens + Cost of Hens + Cost of Roosters = 100)

Since both equations are equal to 100 we can set them equal to each other

C + H + R = .5*C + 1*H + 5*R
C + R = .5*C + 5*R (subtract Hens since both sides are equal)
.5*C = 4* R (isolate remaining variables)
C = 8*R (simplify)

This means that for every 1 Rooster there will be 8 Chickens.
1 + 8 = 9 total
.5*8 + 5*1 = 9 dollars

Since this will always be even in total amount and cost, the remaining amount will be left for Hens

All possible Combinations:

Total C - 8...16...24..32..40..48..56..64..72..80...88
Total H - 91..82..75..64..55..46..37..28..19..10...1
Total R - 1...2....3....4....5....6...7....8....9....10...11

RE: The Chicken Game

schmev — Sat, 29 Jul 2006 09:19:10 GMT

Excellent Richie: You win the fastest award for problem solving that I now post. Somehow, I figured you would solve that because you couldn't resist.

I spend most of my time reading your feedback and I want to say, you are extremely intelligent or "gifted." That was good! Not only are you an asset to this forum, I consider you my friend for your patience and help.

Just a little advanced algebra and solving for three unknowns usually gets it. Well, you took care of that game.

schmev

RE: The Chicken Game

RichieUK — Sat, 29 Jul 2006 07:57:42 GMT

40 chicks = $20
5 roosters= $25
55 hens = $55
..... ......
100 $100

The Chicken Game

schmev — Sat, 29 Jul 2006 06:31:12 GMT

Question:

You have $100 to spend and you want to buy 100 chickens. You have to spend exactly the $100 dollars you have and buy 100 chickens. Chicks are $.50 each, hens are $1.00 each, and roosters are $5.00 each.

You need to buy at least one of each kind and end up with 100 chickens and spend $100.

How many roosters, hens and chicks would you have to buy and spend $100 and end up with a combination of 100 chickens?

Hint: There may be more than one combination!!!

schmev