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.
John has already answered you twice! Do not post this question again.
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Your response is correct. Explanation:
To solve this problem, we can use a system of equations. Let's assign variables to the number of dogs (d) and chickens (c) in the backyard.
From the given information, we know that there are a total of 36 animals, which can be expressed as:
d + c = 36 (Equation 1)
We also know that the total number of legs is 56. Each dog has 4 legs, and each chicken has 2 legs. So, the number of legs can be expressed as:
4d + 2c = 56 (Equation 2)
Now, we can solve this system of equations.
From Equation 1, we can solve for d:
d = 36 - c
Substituting this value of d into Equation 2, we get:
4(36 - c) + 2c = 56
144 - 4c + 2c = 56
-2c = 56 - 144
-2c = -88
c = -88/-2
c = 44
Now, substitute the value of c back into Equation 1 to find d:
d + 44 = 36
d = 36 - 44
d = -8
We have found that there are -8 dogs and 44 chickens in the backyard. Since it doesn't make sense to have negative animals, we can conclude that there is an error in our calculations.
Therefore, the farmer's claim is incorrect because there are 36 animals total, not 56. So, answer choice (a) "It is incorrect because there are 36 animals total, so 4d+2c=36" is the accurate statement.