Statistics help Minimum required sample size

n=24 (farmers) out of a total population of N=200 (farmers)
x_bar(sample mean)=255.00(acres of corn) Standard deviation =100.00(acres of corn)

Based on this information find the minimum required sample size to estimate a 95% confidence interval for the average number of acres devoted to corn production on all dairy farms in this region "U" (population mean) given a maximum allowable error of plus or minus 10.0 acres?

I can figure out what method to solve this problem, please help teach me how to do this thank you!

Since it is sampling from finite population,
Sd of sample mean = Sqrt{sigma^2/n*(N-n)/(N-1)} = Sqrt{10000/n*(200-n)/(199)}
n is such that
1.96*Sqrt{10000/n*(200-n)/(199)} < 10
3.842*{10000/n*(200-n)/(199)} < 100
193.065(200-n) < 100n
200-n < 0.52n
n > 131.58
Least n is 132.