Problem 52 - Prealgebra

Question

Xavier opened a checking account with a deposit of \(\$ 200 .\) During the next week, he wrote checks for \(\$ 65, \$ 83,\) and \(\$ 28\) and made a deposit of \(\$ 50 .\) Write an addition expression for this situation and find the balance in his account.

Step-by-Step Solution

Answer

The final balance in Xavier's account is \( \$74 \).

Step 1: Analyze the Starting Balance

Xavier opens a checking account with an initial deposit of \( \$200 \). This is the starting balance of his account.

Step 2: Express Transactions as Algebraic Operations

Each transaction must be considered as an operation on the account balance. Writing a check deducts money, so checks of \( \\(65 \), \( \\)83 \), and \( \\(28 \) are subtractions. A deposit adds money, so the deposit of \( \\)50 \) is an addition.

Step 3: Write the Addition Expression

Write an expression combining all transactions: \( 200 - 65 - 83 - 28 + 50 \). This expression represents the operations performed on the initial deposit to get the final balance.

Step 4: Calculate the Balance

Solve the expression: \(200 - 65 = 135\), then \(135 - 83 = 52\), then \(52 - 28 = 24\), and finally \(24 + 50 = 74\). Thus, the balance in Xavier's account is \( \$74 \).

Key Concepts

Checking Account

A checking account is a type of bank account that allows people to deposit and withdraw money conveniently. It is often used for everyday spending. When you open a checking account, you will usually start with an initial deposit, just like Xavier did in our example with his $200.
Checking accounts come with features like checks and debit cards, making it easy to make purchases, pay bills, or withdraw cash. They offer a flexible way to manage personal finances.
Unlike savings accounts which focus on earning interest, checking accounts are primarily used for daily transactions. Occasionally, there might also be small fees or requirements attached, such as maintaining a minimum balance.

Transactions

In the context of a checking account, transactions refer to any action that changes the account balance. The two main types of transactions are:

• Deposits: This is money you put into your account. In Xavier's case, he deposited $50 in addition to his initial $200.
• Withdrawals: This can be in the form of using checks, using a debit card, or ATM withdrawals. Every check Xavier wrote counts as a withdrawal: $65, $83, and $28 respectively.

Understanding transactions is vital for managing your account effectively. Keeping track will help prevent overspending and incurring overdraft fees.

Account Balance

An account balance is the amount of money currently available in your checking account after all transactions have been accounted for. It's crucial to keep track of your account balance to ensure you have sufficient funds for your needs.
To calculate the balance, you begin with the starting deposit and then apply all subsequent transactions, considering deposits as additions and withdrawals as subtractions. For Xavier, starting with $200, after accounting for his activities, his balance comes to $74.
Whenever you check your balance, make sure to account for any scheduled or pending transactions that might not yet reflect in the total.

Algebraic Operations

Algebraic operations include addition, subtraction, multiplication, and division. In the context of maintaining a checking account, we primarily use addition and subtraction to represent financial transactions.
Each transaction in a checking account can be expressed as an algebraic operation:

• Addition: Used to represent deposits, such as Xavier’s \(50 deposit.
• Subtraction: Used to represent withdrawals, like the amounts Xavier wrote on checks (\)65, \(83, \)28).

The final expression for a series of transactions is a simplified way to understand the change in balance over time. In Xavier’s case, the expression was: \[ 200 - 65 - 83 - 28 + 50 \]
This formula helps visualize how money flows in and out, leading to a final balance of $74.