A farm has only sheep and geese. It has a total of 58 animals and a total of 150 legs on the animals. How many sheep and geese are on the farm?
s + g = 58
4s + 2g = 150
or
2s + g = 75
subtract them:
s = 17
then g = 41
there are 17 sheep and 41 geese
Well, the sheep and geese should probably count their legs and do some math. But I'm here to help! Let's call the number of sheep 's' and the number of geese 'g'.
Now, we know that a sheep has 4 legs and a goose has 2 legs. So, if we multiply the number of sheep by 4 and the number of geese by 2, we should get a total of 150 legs.
That gives us the equation: 4s + 2g = 150.
Now, we also know that the total number of animals is 58. So we can write another equation: s + g = 58.
Now it's time to solve these equations and find the answer! But let's keep it light, shall we? How about we host a "dance-off" between the sheep and geese to count their legs? Who do you think would win?
Let's assume that the number of sheep on the farm is "x" and the number of geese is "y".
We can set up a system of two equations to represent the given information:
Equation 1: x + y = 58 (since there are a total of 58 animals on the farm)
Equation 2: 4x + 2y = 150 (since each sheep has 4 legs and each goose has 2 legs, the total number of legs is 150)
To solve this system of equations, we can use the method of substitution:
Step 1: Solve Equation 1 for x or y.
Looking at Equation 1, we can solve for x by subtracting y from both sides:
x = 58 - y
Step 2: Substitute the value of x from Step 1 into Equation 2.
Substituting x = 58 - y into Equation 2, we get:
4(58 - y) + 2y = 150
Step 3: Simplify and solve the equation.
Expanding and simplifying the equation:
232 - 4y + 2y = 150
-2y = 150 - 232
-2y = -82
Step 4: Solve for y.
Dividing both sides by -2:
y = -82 / -2
y = 41
Step 5: Solve for x.
Substituting the value of y into Equation 1, we get:
x + 41 = 58
x = 58 - 41
x = 17
Therefore, there are 17 sheep and 41 geese on the farm.
To solve this problem, we can set up a system of equations. Let's assume that the number of sheep on the farm is represented by "s" and the number of geese is represented by "g".
1. We know that the farm has a total of 58 animals. This can be expressed as: s + g = 58.
2. We also know that the total number of legs on the animals is 150. Sheep have 4 legs and geese have 2 legs, so the equation can be written as: 4s + 2g = 150.
Now we have a system of two equations:
Equation 1: s + g = 58
Equation 2: 4s + 2g = 150
There are several methods to solve this system, such as substitution, elimination, or matrices. Let's solve it using the method of substitution:
1. Solve Equation 1 for s: s = 58 - g.
2. Substitute s in Equation 2: 4(58 - g) + 2g = 150.
3. Simplify the equation: 232 - 4g + 2g = 150.
4. Combine like terms: -2g = -82.
5. Solve for g: g = (-82) / (-2) = 41.
Now that we know the number of geese, we can substitute this value back into Equation 1 to find the number of sheep:
s + 41 = 58
s = 58 - 41
s = 17.
Therefore, there are 17 sheep and 41 geese on the farm.