Math CentralQuandaries & Queries


Question from Kamarah, a student:

If a rooster is worth 5 coins and a hen is worth 3 coins and chicks 3 together are worth 1 coin, how many roosters, hen and chicks totaling 100 can be bought with 100 coins?

you must buy at least one of each type of fowl
no fractional fowl
chicks are purchased in multiple of 3
find 3 solutions

Hi Kamarah,

I would try what some educators call guess-and-check but it's much more than guessing, it's intelligent trial and error.

I started thinking about roosters since they are the most expensive. You could spend all 100 coins on roosters but you would only get 20 creatures and you need 100. If you bought 19 roosters it would leave you with 5 coins and the most you could buy with 5 coins would be 15 chick giving 19 + 15 = 34 creatures. again not nearly enough, so lets drop down on the number of roosters to 15 (75 coins) and be more organized by using a table. (I am ignoring the fact that I need hens also but hopefully I can fix that later.)

  roosters hens chicks total
number 15     15
coins spent 75     75

This leaves 25 coins and I could spend them all on 75 chicks giving

  roosters hens chicks total
number 15   75 90
coins spent 75   25 100

which is still too few creatures.

What about 14 roosters?

  roosters hens chicks total
number 14     14
coins spent 70     70

This leaves 30 coins and spending them all on chicks gives

  roosters hens chicks total
number 14   90 104
coins spent 70   30 100

This is too many creatures so I could spend 3 coins on hens giving

  roosters hens chicks total
number 14 1 81 96
coins spent 70 3 27 100

Almost there!

What about 13 rosters? 12 roosters? 11? 10?


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