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| | 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 |
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| | 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 |
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| 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 |
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