There are 14 animals in the field. Some are cows and some are geese. There are 42 legs in all. How many of each animal are in the field?
14=c+g
42=?
Help me figure out the rest of the equation
don't know how many legs each kind of animal has?
4c+2g = 42
To figure out the equation, you need to take into account the number of legs each animal has. Cows have 4 legs, and geese have 2 legs.
Let's assign variables to represent the number of cows and geese in the field. We will use "c" for cows and "g" for geese.
The total number of animals in the field is 14, which can be represented as:
c + g = 14
Now, we need to consider the number of legs. Cows have 4 legs, and geese have 2 legs. So, the total number of legs can be represented as:
4c + 2g = 42
Now we have a system of equations:
c + g = 14
4c + 2g = 42
To solve this system of equations, we can use the method of substitution or elimination. I will use the method of substitution in this example.
Step 1: Solve the first equation for c:
c = 14 - g
Step 2: Substitute the value of c into the second equation:
4(14 - g) + 2g = 42
Step 3: Simplify and solve for g:
56 - 4g + 2g = 42
-2g = 42 - 56
-2g = -14
g = -14 / -2
g = 7
Step 4: Substitute the value of g into the first equation to find the value of c:
c + 7 = 14
c = 14 - 7
c = 7
Therefore, there are 7 cows and 7 geese in the field.