2% of the village died due to an epidemic. A panic set in, during which 14% of the remaining people left the village . If the population is then reduced to 2107, what was it originally?
Oh, looks like the village had quite the KILL-ometer, huh? Alright, let's break it down.
If 2% of the village died due to the epidemic, we can safely assume that 98% survived.
Now, after that, a panic ensued causing 14% of the remaining people to flee. So, we're left with 86% (100% - 14%) of the original population.
If we let 'x' represent the original population size, we can set up an equation to solve this riddle:
0.86x = 2107
Now, let me use my mathematical abilities to calculate the original population for you...drumroll, please...
[Calculating...]
It seems that the original population of the village was approximately **2450** people! Ta-da!
Let's assume the original population of the village is represented by "x".
Step 1: Calculating the number of people who died due to the epidemic
2% of the population died. This means 2% of "x" people died, which is equal to 0.02 * x.
Step 2: Calculating the number of people remaining after the epidemic
The number of people remaining after the epidemic would be the original population "x" minus the number of people who died, which is (x - 0.02 * x).
Step 3: Calculating the number of people who left the village during the panic
14% of the remaining people left the village. This means 14% of (x - 0.02 * x) people left, which is equal to 0.14 * (x - 0.02 * x).
Step 4: Calculating the final population
The final population after people leaving the village would be the remaining population minus the number of people who left, which is (x - 0.02 * x) - (0.14 * (x - 0.02 * x)).
Given that the final population is 2107, we can set up the equation:
(x - 0.02 * x) - (0.14 * (x - 0.02 * x)) = 2107
Simplifying the equation further:
0.98 * x - 0.14 * x + 0.0028 * x = 2107
Combining like terms:
0.8428 * x = 2107
Dividing both sides by 0.8428:
x = 2107 / 0.8428
Calculating x:
x ≈ 2500
Therefore, the original population of the village was approximately 2500.
To find out the original population of the village, we can work backwards.
Let's assume the original population of the village was 'x'.
First, 2% of the village died due to the epidemic. This means (100% - 2%) = 98% of the population remains.
Next, during the panic, 14% of the remaining people left the village. So, (100% - 14%) = 86% of the population remains.
Now, we know that 86% of the original population, which was 'x', is equal to 2107.
Mathematically, we can represent this as: 0.86x = 2107.
To find 'x', we can divide both sides of the equation by 0.86:
x = 2107 / 0.86.
Using a calculator, we find that x is approximately equal to 2450.
Therefore, the original population of the village was approximately 2450.
original number --- x
after epidemic --- .98x are left
14% of those leave, leaving
(.86)(.98x)
.86(.98x) = 2107
x = 2107/(.86(.98)) = 2500