Bank Account Balances: Calculate Total Accounts with Specific Figures

At the bank, there are several of accounts.

The balance of 3 accounts is over $300. Several accounts are under$200. An identical number have less than $25.<br><br>How many accounts in total are in the red if the bank has$0?

We need to determine how many accounts are "in the red." Assuming a "zero balance" at the bank means total assets equal total liabilities, "in the red" would consist of negative account balances.

Define variables for the problem: let $x$ be the number of accounts having less than $25, and since these are identical to the ones having less than$200, let this also be $x$.

We have the following account categories:

• 3 accounts with a balance > $300
• $x$ accounts with a balance < $200 and also <$25
• The bank balance totals 0.

Calculate the total balances:

• Total excess balance from 3 accounts = \( 3 \times 300 = 900 or more.
• Assume accounts $x$ have a balance of around $-100$ (since many accounts are likely negative if overall balance retains 0).

The equation for balance is:

Solving:

Solve for $x$:

The accounts in the red (negative) are the ones under $200 but less than$25, similar in number.

The total is:
Accounts under $200 contribute twice, counting for less than$25 and up to 200 multiple. Therefore, our calculation confirms these 8 accounts are in debt to the bank as accounting overlaps set at zero balance state with total configuration.

Therefore, the number of accounts in the red is \( \boxed{8} .