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.
I just answered this below with quite a bit of detail.
Your response is incorrect. The correct answer is b.) It is incorrect because there are 56 legs total, so d+c=56.
Let's break it down step-by-step to understand why:
1. Let d represent the number of dogs and c represent the number of chickens.
2. Each dog has 4 legs, so the total number of dog legs can be represented as 4d.
3. Each chicken has 2 legs, so the total number of chicken legs can be represented as 2c.
4. The problem states that there are a total of 56 legs, so we can create the equation 4d + 2c = 56 to represent this information.
Therefore, the farmer's claim 4d + 2c = 56 is accurate.
To determine the accuracy of the farmer's claim, let's analyze the given information and the equation: 4d + 2c = 56.
We know that there are a total of 36 animals in the backyard. Let d represent the number of dogs and c represent the number of chickens. So, the equation 4d + 2c = 56 represents the total number of legs (which is 56 in this case since each dog has 4 legs and each chicken has 2 legs).
To check the accuracy of the claim, we need to see if the equation accurately represents the given information. If the equation holds true, then it means that the total number of legs is indeed 56.
Let's substitute the values to check: If we take -8 as the number of dogs (d = -8) and 44 as the number of chickens (c = 44), the equation becomes 4(-8) + 2(44) = 56.
Simplifying the equation: -32 + 88 = 56.
So, the equation holds true, and the total number of legs is indeed 56.
Therefore, the accuracy of the farmer's claim is described by statement c.) It is correct because there are 56 legs total, so 4d + 2c = 56.