A flock of geese is flying while another goose is flying past it. The goose asks the leader of the flock how many they are. The leader answers:
"Us, plus us, plus half of us, plus a quarter of us, plus myself make the flock 100 geese. How many are we?
x+x+x/2+x/4 + 1 = 100
8x+x2x+x+4x=x100
x=36
check:
36+36+18+9+1 = ????
Thanks
Let "us"=a
a + a + a/2 +a/4 + 1 = 100
a + a + a/2 +a/4 = 99
2a + a/2 +a/4 = 99
a (2 + 0.5 + 0.25) = 99
a (2.75) = 99
a = 36
To find the number of geese in the flock, we need to break down the information given by the leader of the flock. Let's go step by step:
1. The leader says, "Us." This means the current number of geese in the flock is represented as "Us."
2. Next, the leader says, "plus us." This means we need to add the current number of geese in the flock, which is "Us," to the existing total.
3. The leader continues, "plus half of us." This means we need to add half of the current number of geese in the flock to the existing total. Mathematically, half of "Us" is represented as (1/2) * Us.
4. The leader then says, "plus a quarter of us." This means we need to add a quarter of the current number of geese in the flock to the existing total. Mathematically, a quarter of "Us" is represented as (1/4) * Us.
5. Finally, the leader adds, "plus myself." This means we need to add one more goose, which is the leader, to the existing total.
The equation can be written as:
Us + Us + (1/2) * Us + (1/4) * Us + 1 = 100
Now, let's simplify the equation to find the value of "Us":
Combining like terms, we have:
(2 + 1/2 + 1/4) * Us + 1 = 100
To simplify the fraction, we convert the mixed number into an improper fraction:
(2 + 1/2 + 1/4) * Us + 1 = 100
(4/2 + 1/2 + 1/4) * Us + 1 = 100
(8/4 + 2/4 + 1/4) * Us + 1 = 100
(11/4) * Us + 1 = 100
Now, we isolate "Us" by subtracting 1 from both sides of the equation:
(11/4) * Us + 1 - 1 = 100 - 1
(11/4) * Us = 99
To solve for "Us," we divide both sides of the equation by (11/4):
(11/4) * Us / (11/4) = 99 / (11/4)
Us = (99 / (11/4))
Performing the division:
Us = 99 * (4/11)
Us = 36
Therefore, the flock consists of 36 geese.