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Chapter 3: Problem 3

Rich has \(t\) dollars in his checking account. On June \(3,\) he deposited \(w_{1}, h,\) and \(v\) dollars, and cashed a check for \(k\) dollars. Write an algebraic expression that represents the amount of money in his account after the transactions.

Short Answer

Expert verified
The algebraic expression that describes the amount of money in Rich's account after all transactions is \(t + w_{1} + h + v - k\).

Step by step solution

01

Initial amount in the account

Rich has initially \(t\) dollars in his checking account. This is the starting point for all the upcoming calculations.
02

Transactions affecting the account

On June 3, Rich deposited \(w_{1}, h,\) and \(v\) dollars. These deposits increase his balance. Therefore, they're added to the starting amount \(t\). On the same day, he also cashed a check for \(k\) dollars. This means that \(k\) dollars are taken from his account, decreasing his balance. Therefore, \(k\) dollars are subtracted from the account balance.
03

Final algebraic expression

The algebraic expression that represents the amount of money in his account after the transactions is \(t + w_{1} + h + v - k\). This account for the starting balance \(t\), the increases \(w_{1}, h, v\), and the decrease \(k\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Financial Transactions
Financial transactions can have varying effects on one's account balance. When discussing Rich's checking account, we're dealing with basic transactions such as deposits and withdrawals. A deposit increases the account balance, helping you grow the amount of money available. On the other hand, a withdrawal, like cashing a check, reduces the balance.
Financial transactions in algebra involve representing these increases and decreases numerically in an expression. Each deposit is a positive increase, while each withdrawal is a negative one. This simple math concept allows us to keep track of money flow using variables, crucial for managing personal finances.
Balance Calculation
Balance calculation involves summing up all the financial activities to find out the final amount in an account. To calculate Rich鈥檚 balance after the given transactions, we need to:
  • Start with the initial amount, which is the balance before any transaction happens.
  • Add the amounts from the deposits because they contribute to increasing the balance.
  • Subtract the amount for cashing a check, as this represents money leaving the account.
This gives us the expression: \[ t + w_1 + h + v - k \]Where:
  • \( t \) is the initial balance in the checking account.
  • \( w_1, h, \) and \( v \) are the amounts deposited 鈥� thus added to the initial balance.
  • \( k \) is the amount of the check cashed, thus subtracted from the balance.
Ultimately, the correct balance calculation ensures accurate tracking of all activity recorded over time.
Variable Representation
Variable representation in algebra helps in expressing real-world problems in mathematical form, making them easier to manipulate and solve. In the context of Rich鈥檚 transactions, each amount of money is represented by a different variable:
  • The amount Rich starts with is represented by the variable \( t \).
  • Deposits are shown as \( w_1, h, \) and \( v \), each signifying a different deposit operation on the account.
  • The check cashed is denoted by \( k \), which is deducted from the total.
By using variables, we can create an algebraic expression that captures the effect of all transactions on Rich鈥檚 account. This enables a clear and flexible way to represent and solve problems encountered in financial settings. Variables allow us to generalize the problem for any values, making the solution versatile.

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Most popular questions from this chapter

Mike deposits \(\$ 5,000\) in a three-year \(\mathrm{CD}\) account that yields 3.5\(\%\) interest, compounded weekly. What is his ending balance at the end of three years?

Zoe creates a spreadsheet to make simple interest calculations. The user inputs values for the principal, rate, and time in years in row 2. Write each formula. a. For A2 to compute the interest. b. For B2 to compute the principal. c. For C2 to compute the interest rate. d. For D2 to compute time in years, given the interest, rate, and the principal. e. For E2 to compute the time in months, given the time in years.

Bob wants \(\$ 50,000\) at the end of 7 years in order to buy a car. If his bank pays 4.2\(\%\) interest, compounded annually, how much must he deposit each year in order to reach his goal?

When Abram was born, his parents put \(\$ 2,000\) into an account that yielded 3.5\(\%\) interest, compounded semiannually. When he turns 16 , his parents will give him the money to buy a car. How much will Abram receive on his 16th birthday?

Ken filled out this information on the back of his bank statement. Find Ken's revised statement balance. Does his account reconcile? $$\begin{array}{|l|l|}\hline \text { Checking Account Summary } \\ \hline \text { Ending Balance } & {\$ 197.10} \\ \hline \text { Deposits } & {+\$ 600.00} \\ \hline \text { Checks Outstanding } & {-\$ 615.15} \\ \hline \text { Revised Statement Balance } & {} \\ \hline \text { Check Register Balance } & {\$ 210.10} \\ \hline\end{array}$$
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