Chickens And Rabbits
Chickens and Rabbits
The problem states there are some chickens and some rabbits in a barnyard. It also states that there are 50 heads and 120 legs on these chickens and rabbits. The problem asks how many chickens and rabbits are in the barnyard. There are 10 rabbits and 40 chickens in the barnyard.
You must first analyze the problem and identify your elements; if each chicken and each rabbit has one head, the number of chickens and dogs together is 50. Each chicken has two legs and each rabbit has four legs; so together the 50 animals have 120 legs.
Check to see if the problem has a possible solution. The minimum number of legs possible would be if all 50 animals were chickens; that would be 50*2=100 legs. The solution is derived by multiplying 50 the number of heads by 2 the number of legs a chicken has. The highest number possible of legs would be if all 50 animals were rabbits; that would be 50*4= 200. Multiplying 50 the number of heads by 4 the number of legs a rabbit has. Since 120 the number of legs altogether of rabbits and chickens is between 100 (minimum number of legs possible if 50 animals were chickens) and 200 (maximum number of legs if all 50animals were rabbits), the problem has a solution.
The first method we will use to solve the problem will be numeric. We will guess that all 50 animals are chicken. We have already determined that this would give us a total of 100. But we need 120 legs, so we are short by 20 legs. We determine this by subtracting 120 legs minus 100 legs. 120-100 =20 legs.
Now imagine we replace one chicken with a rabbit. The replaced chicken had two legs, and the rabbit has four legs, so we now have two more legs than before. Each time we replace a chicken with another rabbit we gain two more legs. So start with a “guess” of 50 chickens and 0 rabbits, which will leave you with 20 legs short of what you need to solve the problem. But you will find that each time that you replace a chicken with a rabbit you will gain two
The problem states there are some chickens and some rabbits in a barnyard. It also states that there are 50 heads and 120 legs on these chickens and rabbits. The problem asks how many chickens and rabbits are in the barnyard. There are 10 rabbits and 40 chickens in the barnyard.
You must first analyze the problem and identify your elements; if each chicken and each rabbit has one head, the number of chickens and dogs together is 50. Each chicken has two legs and each rabbit has four legs; so together the 50 animals have 120 legs.
Check to see if the problem has a possible solution. The minimum number of legs possible would be if all 50 animals were chickens; that would be 50*2=100 legs. The solution is derived by multiplying 50 the number of heads by 2 the number of legs a chicken has. The highest number possible of legs would be if all 50 animals were rabbits; that would be 50*4= 200. Multiplying 50 the number of heads by 4 the number of legs a rabbit has. Since 120 the number of legs altogether of rabbits and chickens is between 100 (minimum number of legs possible if 50 animals were chickens) and 200 (maximum number of legs if all 50animals were rabbits), the problem has a solution.
The first method we will use to solve the problem will be numeric. We will guess that all 50 animals are chicken. We have already determined that this would give us a total of 100. But we need 120 legs, so we are short by 20 legs. We determine this by subtracting 120 legs minus 100 legs. 120-100 =20 legs.
Now imagine we replace one chicken with a rabbit. The replaced chicken had two legs, and the rabbit has four legs, so we now have two more legs than before. Each time we replace a chicken with another rabbit we gain two more legs. So start with a “guess” of 50 chickens and 0 rabbits, which will leave you with 20 legs short of what you need to solve the problem. But you will find that each time that you replace a chicken with a rabbit you will gain two