Out on my street, there are a certain number of pigeons sitting on telephone poles. If there were exactly 2 pigeons sitting on each telephone pole, then 1 pigeon would have no space to sit on. If there were exactly 3 pigeons sitting on each telephone pole, then there would be 1 telephone pole with no pigeons on. How many pigeons were there
To find the number of pigeons, we need to solve the problem using a system of equations.
Let's assume there are "x" telephone poles and "y" pigeons.
According to the first scenario, if there were exactly 2 pigeons sitting on each telephone pole, then one pigeon would have no space to sit on. This means that there would be x - 1 pigeons in total.
Equation 1: y = 2(x - 1)
According to the second scenario, if there were exactly 3 pigeons sitting on each telephone pole, then there would be 1 telephone pole with no pigeons on. This means that there would be x - 1 poles filled with pigeons.
Equation 2: y = 3(x - 1)
Now we have a system of equations. We can solve them simultaneously to find the values of x and y.
Equation 1: y = 2x - 2
Equation 2: y = 3x - 3
Since both equations are equal to y, we can set them equal to each other:
2x - 2 = 3x - 3
Now, solve for x:
x = 1
Substitute the value of x back into one of the equations to find y:
y = 2(1) - 2
y = 0
Therefore, there is only 1 pigeon sitting on the telephone pole.