Let \( E \) be the amount of money that Emma had in her account when they arrived at the bank.
Since Alexis had three times as much money as Emma at the start, we can express Alexis's amount as: \[ A = 3E \] where \( A \) is the amount of money Alexis had.
After Alexis withdrew $100, the amount in her account becomes: \[ A - 100 = 3E - 100 \]
At the same time, after Emma deposited $25, the amount in her account becomes: \[ E + 25 \]
According to the problem, after these transactions, they both had the same amount of money in their accounts: \[ 3E - 100 = E + 25 \]
Now, we can solve for \( E \) by first isolating \( E \): \[ 3E - E = 25 + 100 \]
This simplifies to: \[ 2E = 125 \]
Dividing both sides by 2 gives: \[ E = 62.5 \]
Thus, Emma had \( \boxed{62.5} \) dollars in her account when they got to the bank.
To verify, we can calculate Alexis's initial amount: \[ A = 3E = 3 \times 62.5 = 187.5 \]
After Alexis withdraws $100: \[ A - 100 = 187.5 - 100 = 87.5 \]
After Emma deposits $25: \[ E + 25 = 62.5 + 25 = 87.5 \]
Both amounts are equal, confirming that Emma had \( \boxed{62.5} \) dollars in her account when they got to the bank.