In a farm, the number of sheep were $\frac{5}{7}$ the number of cows. $21$ new sheep were brought into the farm while $7$ cows were removed. At the end, the number of cows became $\frac{3}{4}$ the number of sheep. Determine the number of sheep at the beginning. 
Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle