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?
If there were exactly 2 pigeons sitting on each telephone pole, then 1 pigeon would have no space ....the number of pigeons is odd. And, numberpigions=numberpoles*2+1
TIf there were exactly 3 pigeons sitting on each telephone pole, then there would be 1 telephone pole with no pigeons on...means 3*poles-1=number pigeosn
Pig=2Poles+1
Pig=3Poles-1
subtract equation 1 from 2
0=poles-2 or poles=2
pigeons=5
Pi=2Po+1,
Pi=3(Po+1)
after solving we get the result as
Pi=9
and
Po=4
To find out how many pigeons there were, we can use algebraic reasoning. Let's assume there are 'x' telephone poles on your street.
According to the information provided, if there were exactly 2 pigeons sitting on each telephone pole, then there would be 1 pigeon with no space to sit. This means the total number of pigeons in this scenario would be 2x - 1.
Similarly, if there were exactly 3 pigeons sitting on each telephone pole, then there would be 1 telephone pole with no pigeons on. In this scenario, the total number of pigeons would be 3x - 1.
Since these two situations describe the same number of pigeons, we can set up an equation based on the given information:
2x - 1 = 3x - 1
By simplifying the equation, we find:
2x = 3x
Subtracting 2x from both sides, we have:
0 = x
So, there are zero telephone poles on your street. This implies that there were no pigeons on your street.