Tom have 100 geese and cows on his far. All in total there are 340 legs. How many geese and how many cows are there.
g + c = 100
2g + 4c = 340
or g + 2c = 170
subtract them ....
c = 70
thus g = 30
check my answer. I obviously have 100 animals, but do
I have 340 legs?
There are X geese and Y cows.
Eq1: x + y = 100.
Eq2: 2x + 4y = 340 Legs.
Multiply Eq1 by -2 and add the Eqs:
-2x - 2y = -200
2x + 4y = 340
Sum: 2y = 140
Y = 70 Cows.
In Eq1, replace Y with 70 and solve for X.
To solve this problem, we need to set up a system of equations based on the given information.
Let's assume the number of geese is represented by "x" and the number of cows is represented by "y."
From the problem statement, we know that:
1. A goose has 2 legs.
2. A cow has 4 legs.
3. The total number of animals (geese + cows) is 100.
4. The total number of legs on the farm is 340.
Based on the above information, we can set up the following equations:
Equation 1: x + y = 100 (since the total number of animals is 100)
Equation 2: 2x + 4y = 340 (since the total number of legs is 340)
We now have a system of two equations with two variables.
To solve, we can either use substitution or elimination.
Let's use elimination to solve this system:
Multiply Equation 1 by 2, which gives us:
2x + 2y = 200 (Equation 3)
Next, subtract Equation 3 from Equation 2:
2x + 4y - (2x + 2y) = 340 - 200
2x + 4y - 2x - 2y = 140
2y = 140
Divide both sides of the equation by 2:
y = 70
Now we can substitute the value of y back into Equation 1 to solve for x:
x + 70 = 100
x = 100 - 70
x = 30
Therefore, there are 30 geese and 70 cows on the farm.