Can you help with the question below?

Question

~~A team has fewer than 10 members. A total of 62.5 percent of the team is from Stanley, the rest of the members are from Boyd. What is the smallest possible number of players that can join the team to bring the percentage who are from Stanley to exactly 55 percent?

Answer 1

62.5% is 5/8, so we can let S=Stanley members and B=Boyd members. The total in the team is T. S+B=T and S=5T/8, so B=3T/8.
If the team takes N new members then the percentage of Stanley members is S/(T+N)=55/100=5T/(8(T+N))=55/100.
Divide both sides by 5: T/8T+8N=11/100. Cross-multiply: 100T=88T+88N. Divide through by 4: 25T=22T+22N.
N=3T/22. N must be a whole number, so T=22 is the lowest value and N=3. However, if T=22, it exceeds 10 and 5/8 of 22=55/4 which is not a whole number, so the lowest value for T would need to be 88, made up of 55 Stanley members, and N=12, making the new team membership 100, with 55 Stanley members.