Problem 41 - Elementary Algebra

Question

Translate each sentence to a mathematical statement and then simplify. Mandy made a \(\$ 200\) deposit into her checking account on Tuesday. She then wrote 4 checks for \(\$ 50.00, \$ 125.00, \$ 60.00,\) and \(\$ 45.00 .\) How much more than her deposit did she spend?

Step-by-Step Solution

Answer

Mandy spent $80 more than her deposit.

Step 1: Define Variables and Equations

First, determine the total amount that Mandy deposited and the total amount of the checks she wrote. The deposit amount is \(200, and the total expense from checks is the sum of \(\\)50.00 + \\(125.00 + \\)60.00 + \$45.00\).

Step 2: Calculate Total Spending from Checks

Calculate the sum of the amounts from all the checks. Add \(\\(50 + \\)125 + \\(60 + \\)45\). This calculation gives the total spending from checks.

Step 3: Simplify the Mathematical Statement

Calculate \(50 + 125 + 60 + 45 = 280\). Thus, Mandy spent \(\$280\) in total by writing checks.

Step 4: Determine Amount Spent Over the Deposit

Subtract the deposit amount from the total spending: \(280 - 200\). This represents how much more money Mandy spent than deposited.

Step 5: Simplify the Final Result

Perform the subtraction \(280 - 200 = 80\). This means Mandy spent \(\$80\) more than her deposit.

Key Concepts

Algebraic Expressions

Algebraic expressions are a fundamental concept in mathematics that allow us to represent real-world situations using mathematical language. In the context of Mandy's financial problem, we use algebraic expressions to model her transactions. For example, we describe her deposit with just a number, such as \(200\), and her checks using another expression, like \(50 + 125 + 60 + 45\). By setting up these expressions, we can easily illustrate how much money she deposited and how much she spent.

To translate a situation into an algebraic expression:

• Identify all the numerical values associated with the problem.
• Determine the operations needed, such as addition or subtraction.
• Create expressions that relate one group of values to another.

Algebraic expressions help us simplify and solve problems by providing a clear mathematical framework to work within.

Financial Literacy

Understanding financial literacy is crucial, as it helps individuals make informed and effective financial decisions. In Mandy's situation, financial literacy involves managing her checking account by keeping track of deposits and expenditures. Whether an individual is balancing a budget or simply recording transactions like Mandy’s, being financially literate can prevent overspending.

Financial literacy involves:

• Understanding how to manage money and make investments wisely.
• Knowing how to track spending and create a budget.
• Recognizing the long-term effects of financial decisions.

By practicing good financial management, individuals like Mandy can avoid financial pitfalls by budgeting accurately and ensuring that expenses do not exceed income.

Arithmetic Operations

Arithmetic operations form the basis of everyday mathematics. In simple terms, these are operations like addition, subtraction, multiplication, and division. In Mandy's case, arithmetic operations play a vital role as we compute her total spending with addition and determine her net financial impact using subtraction.

To solve problems involving arithmetic operations:

• Use addition to find the total of several numbers, such as Mandy’s total check amounts.
• Apply subtraction to compare two quantities, for instance, subtracting Mandy’s deposit from her total spending.

These operations are essential when evaluating Mandy’s financial transactions as they allow us to track totals and differences accurately, ensuring no errors in financial calculations.