A farmer has dogs and chickens running around in his backyard. There are a total of 36 animals, and the farmer counts a total of 56 legs. The farmer can use a system of equations to determine how many of each animal there are. He claims that one of the equations in the system is 4d+2c=56.
Which statement describes the accuracy of the farmer's claim?
a.) It is incorrect because there are 36 animals total, so 4d+2c=36.
b.) It is incorrect because there are 56 legs total, so d+c=56.
c.) It is correct because there are 56 legs total, so 4d+2c=56.
d.) It is incorrect because there are 36 animals total, so d−c=36.
My response is that they are correct with -8 dogs, and 44 chickens, which is answer choice c.
It is c, because dogs have 4 legs and chickens have 2 legs and there are 56 legs in all.
You can't have -8 dogs or 1/2 of either. You are just guessing right now.
You would need d + c =36 along with 4d+2c + 56 to find the exact number of dogs and chickens.
You would eliminate one variable and solve for the other. However, that isn't asked for here. It probably will be required later on.
To solve this problem, we can set up a system of equations based on the information given. Let's use 'd' to represent the number of dogs and 'c' to represent the number of chickens.
The total number of animals is given as 36, so we can set up the equation:
d + c = 36
Since each dog has 4 legs and each chicken has 2 legs, the total number of legs can be represented as 4d + 2c. According to the problem, the farmer counts a total of 56 legs, so we can set up the equation:
4d + 2c = 56
Now, let's examine the answer choices:
a) It is incorrect because there are 36 animals total, so 4d + 2c = 36.
This option is incorrect because the problem specifically states that the farmer counted 56 legs, not 36 animals.
b) It is incorrect because there are 56 legs total, so d + c = 56.
This option is incorrect because the problem states that there are a total of 36 animals, not 56 legs.
c) It is correct because there are 56 legs total, so 4d + 2c = 56.
This option correctly represents the equation that reflects the total number of legs.
d) It is incorrect because there are 36 animals total, so d - c = 36.
This option is incorrect because it uses a subtraction operation instead of addition, and it does not represent the total number of legs.
Therefore, the accurate statement is c) It is correct because there are 56 legs total, so 4d + 2c = 56.
Now, to find the specific values of 'd' and 'c', we can solve this system of equations. By substituting the value of 'd' from the first equation (d + c = 36) into the second equation (4d + 2c = 56), we can solve for 'c'. Once we find the value of 'c', we can substitute it back into the first equation to find 'd'. By solving these equations simultaneously, we can find the number of dogs and chickens.