Question

"A farmer raises goats and chickens on his farm. He has a total of 47 animals and altogether his animals have 118 legs. This can be set up as a system such that

G+C = 47
4G + 20 = 118
Kelly graphed these two lines with Gasx and Casy and got an intersection point at (12.35). What does that mean in the context of the problem?"

Answer 1

The intersection point at (12, 35) means that there are 12 goats and 35 chickens on the farmer's farm.

Step-by-step explanation:

The intersection point at (12, 35) means that there are 12 goats and 35 chickens on the farmer's farm. This is the solution to the system of equations G + C = 47 and 4G + 20C = 118.

Using the first equation G + C = 47, we can substitute G with 47 - C in the second equation to get 4(47 - C) + 20C = 118.

Simplifying this equation, we have 188 - 4C + 20C = 118. Combining like terms, we get 16C = 30. Solving for C, we find that C = 35.

Substituting C = 35 into the first equation G + 35 = 47, we can solve for G and find that G = 12.