Let's solve this problem step-by-step.
1. Step 1: Define the initial number of cows.
Let the initial number of cows be [tex]\( x \)[/tex].
2. Step 2: Calculate the cows remaining after 10% died.
If 10% of the cows died in the first year, then 90% of the cows are still alive.
[tex]\[
\text{Remaining cows after the first year} = 0.9 \times x
\][/tex]
3. Step 3: Calculate the cows remaining after 12.5% of the remaining cows died in the second year.
12.5% of the remaining cows die in the second year. To find the number of cows that died in the second year, we need 12.5% of the cows remaining after the first year.
[tex]\[
\text{Cows died in the second year} = 0.125 \times (0.9 \times x)
\][/tex]
Therefore, the cows left after the second year are:
[tex]\[
\text{Remaining cows after the second year} = (0.9 \times x) - (0.125 \times 0.9 \times x)
\][/tex]
Simplify:
[tex]\[
\text{Remaining cows after the second year} = 0.9x - 0.1125x = 0.7875x
\][/tex]
4. Step 4: Set up the equation using the given final number of cows.
According to the problem, after both years, there are 63 cows remaining.
[tex]\[
0.7875x = 63
\][/tex]
5. Step 5: Solve for [tex]\( x \)[/tex].
[tex]\[
x = \frac{63}{0.7875}
\][/tex]
Calculate:
[tex]\[
x = 80
\][/tex]
So, the villager originally had [tex]\( 80 \)[/tex] cows.
