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?
Let x = # of poles
2x + 1 = 3(x_1)
2 pigeons per pole with 1 pigeon
3 pigeons per poles with 1 less pole.
2x + 1 = 3x -3
x = 4 poles
You have 2 pigeons per pool = 8 pigeons + one left over = 9 pigeons.
3 pigeons per pole = 9 pigeons.
It looks like we have nine pigeons.
Let's start by solving the first scenario where there are exactly 2 pigeons sitting on each telephone pole and 1 pigeon has no space to sit on. In this case, if we assume there are a total of x telephone poles, then the number of pigeons would be 2 multiplied by the number of telephone poles (x).
So, the number of pigeons in the first scenario can be represented as 2x.
Now, let's move on to the second scenario where there are exactly 3 pigeons sitting on each telephone pole, and 1 telephone pole has no pigeons on it. In this case, if we again assume there are x telephone poles, the number of pigeons would be 3 multiplied by the number of telephone poles minus 1 because one telephone pole has no pigeons.
So, the number of pigeons in the second scenario can be represented as 3x - 1.
To find the actual number of pigeons, we need to find a value of x that satisfies both scenarios. We can set these two equations equal to each other and solve for x:
2x = 3x - 1
By subtracting 2x from both sides, we get:
-x = -1
And by multiplying both sides by -1, we get:
x = 1
Substituting this value back into either equation, we find:
2(1) = 3(1) - 1
2 = 2
Therefore, there is 2 pigeons on each telephone pole, and there is a total of 2 pigeons.