frank has 100 geese and cows on his farm. The animals have a total of 340 legs. How many geese and cows does frank have?
Well, Frank certainly has quite the farm! Let me do some quick calculations here. If we let "g" represent the number of geese and "c" represent the number of cows, we can set up the following equation: 2g + 4c = 340 (since geese have 2 legs and cows have 4 legs).
Now, let's solve this equation in a funny way! I'll call in my math circus friends to lend a helping hand.
*Clowns juggling numbers, please come to the stage!*
Okay, let's see. We have 100 geese which would contribute 2g legs, and cows with 4c legs. So, in total, we have:
2g + 4c = 340
But wait! Can we simplify this equation a bit further? Of course!
Let's divide the whole equation by 2:
g + 2c = 170
Now, we have another equation that relates geese and cows on Frank's farm. It looks like the geese and cows together make 170.
Hmm, let's have the acrobatic clowns rush in with their balancing act!
After some fancy calculations, we know that Frank has 30 geese (g) and 70 cows (c) on his farm.
So, Frank has 30 geese and 70 cows, making a grand total of 100 animals on his farm. Those geese must be quite the travelers with such long necks!
To solve this problem, we can set up a system of equations based on the given information.
Let's say the number of geese is represented by "g" and the number of cows is represented by "c". We're given that Frank has a total of 100 geese and cows, so we can set up the first equation:
g + c = 100
Next, we're given that the animals have a total of 340 legs. Geese have 2 legs each, and cows have 4 legs each. So, the second equation can be written as:
2g + 4c = 340
Now we can solve the system of equations using substitution or elimination. Let's use substitution.
First, solve the first equation for "g":
g = 100 - c
Now substitute this expression for "g" in the second equation:
2(100 - c) + 4c = 340
Simplify and solve for "c":
200 - 2c + 4c = 340
2c = 340 - 200
2c = 140
c = 70
Now substitute the value of "c" back into the first equation to find "g":
g + 70 = 100
g = 100 - 70
g = 30
Therefore, Frank has 30 geese and 70 cows on his farm.
To solve this problem, let's assign variables to the number of geese and cows Frank has. Let's say the number of geese is represented by "G" and the number of cows is represented by "C".
We are given two pieces of information:
1) Frank has 100 geese and cows in total: G + C = 100.
2) The animals have a total of 340 legs. Since each goose has 2 legs and each cow has 4 legs, the total number of legs can be represented as 2G + 4C = 340.
Now, we have a system of two equations:
Equation 1: G + C = 100
Equation 2: 2G + 4C = 340
We can solve this system of equations to find the values of G and C.
To eliminate G, let's multiply Equation 1 by 2:
2(G + C) = 2(100)
2G + 2C = 200
Now, we can subtract this equation from Equation 2 to get rid of G:
2G + 4C - (2G + 2C) = 340 - 200
2G + 4C - 2G - 2C = 140
2C - 2C = 140
The "2C" term cancels out, leaving us with:
0 = 140
This equation tells us that 0 = 140, which is not true. This means there is no solution to the system of equations.
Therefore, there must be an error in the problem statement or the given information. The total number of legs and the number of animals do not match up.
assuming no one legged geese (I had a one legged duck once), or no cows with less or more than four legs..
340=4*C+2*G
C+G=100