A pigeon runs into a flock of pigeons and asks their leader what is your number in this flock? The leader replays: I am not suppose to tell you our exact number, but if you take twice our number and add a half of our number and still add another quarter of our number plus yourself would be 100. How many pigeons were in that flock? Write an equation and solve it
Let x be the number of pigeons in the flock.
2x + x/2 + x/4 +1 = 100
(11/4) x = 99
Solve that.
can I have a hint?
is there another way to solve this??
I am not sure how to solve this one
Multiply both sides of the equality sign by (4/11).
To answer this question, we need to set up an equation based on the information given and then solve it.
Let's represent the number of pigeons in the flock as "x". According to the leader's response, we can translate the given information into an equation:
2x + (1/2)x + (1/4)x + 1 = 100
This equation represents adding the twice the number of pigeons, half the number of pigeons, a quarter of the number of pigeons, and 1 (representing yourself). The sum of these values equals 100.
Now, let's simplify and solve the equation step by step:
Multiplying through by the common denominator of 4:
8x + 2x + x + 4 = 400
Combining like terms:
11x + 4 = 400
Subtracting 4 from both sides of the equation:
11x = 396
Dividing both sides by 11:
x = 36
Therefore, there were 36 pigeons in the flock.