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| Math Central | Quandaries & Queries |
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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? notes: |
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?
Penny
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