The Farm Yard Problem

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The Farm Yard Problem In class we are doing a portfolio called “The Farm Yard Problem”. In this problem a farmer has some pigs and chickens. After going through and counting, the farmer found that all together the chickens and pigs have 70 heads and 200 legs. Since this is a portfolio, the question I am supposed to answer is: How many pigs and chickens does the farmer have? For the answer to this portfolio question, I found there was 40 total chickens and 30 total pigs on this persons farm. The first thing I did to find the answer to this portfolio was make a table. In this table there was a column for chickens, one for pigs, another for legs, and a final one for heads. Since I knew there was 70 heads, and both pigs and chickens each only have one head, I knew there was a total of 70 animals. This meant that however many chickens or pigs there were, the other would have the number that when combined makes 70 (ex. If there were 2 pigs there would be 68 chickens). Like I said, I already knew that whatever number I put in for chickens would have to make 70 when added to the number of pigs and vise-versa, so my first thought was to try numbers like 10 and 60 or 20 and 50. Below you'll see my table. The Farm Yard Problem Table Chickens | Pigs | Legs | Heads | 0 | 70 | 280 | 70 | 10 | 60 | 260 | 70 | 20 | 50 | 240 | 70 | 30 | 40 | 220 | 70 | 40 | 30 | 200 | 70 | 50 | 20 | 180 | 70 | 60 | 10 | 160 | 70 | 70 | 0 | 140 | 70 | As you can see in my table above, there are 40 chickens and 30 pigs to total the 200 legs and 70 heads. To find this I knew that chickens each only have two legs, and pigs have four. I took that information and plugged it into the table so for the first row there would turn out to be

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