Problem 41 - Intermediate Algebra

Question

Solve each formula for the specified variable. \(Q=\frac{A-I}{L}\) for \(A\) (from banking)

Step-by-Step Solution

Answer

The equation for \( A \) is \( A = QL + I \).

Step 1: Understand the Equation

The given formula is \( Q = \frac{A-I}{L} \), where the task is to solve for the variable \( A \). The other variables \( Q, I, \) and \( L \) are known quantities.

Step 2: Multiply by L to Eliminate the Denominator

To eliminate the fraction, multiply both sides of the equation by \( L \). This gives \( QL = A - I \).

Step 3: Isolate A

Rearrange the equation to solve for \( A \). Add \( I \) to both sides to isolate \( A \). This results in \( A = QL + I \).

Key Concepts

Solving for a Variable

When you are given an equation involving several variables, and need to solve for one specific variable, the process is known as "solving for a variable." To achieve this, you need to rearrange the equation so that the variable appears alone on one side of the equation. Let's take a simple example using the formulated equation from the exercise.To solve for the variable \( A \) in the equation \( Q = \frac{A-I}{L} \):

• Identify the target variable: In this case, \( A \).
• Rearrange the equation: Eliminate fractions by multiplying by the denominator \( L \).
• Manipulate the equation by using inverse operations (such as addition or subtraction) to isolate the targeted variable \( A \) on one side.

This process requires familiarity with algebraic manipulation, allowing you to handle complex formulas confidently.

Banking Formulas

Banking formulas are used extensively to calculate variables in financial equations. They often involve operations related to interest, loans, or investments. In our exercise, the formula features terms like \( A \), \( I \), \( L \), which may represent accumulation, initial investment, and interest or loan amount, respectively.These kinds of formulas:

• Help in solving various financial problems, like determining final account balances or loan payments.
• Typically use algebraic expressions, which require manipulation to find unknown quantities.
• Often need precise calculations since they deal with real-world monetary scenarios.

Understanding these formulas allows you to better manage personal or business finances, optimizing financial decision-making.

Intermediate Algebra

Intermediate algebra acts as a bridge between basic algebra and more advanced mathematics, providing foundational skills necessary for solving complex equations. It often includes:

• Working with polynomials, rational expressions, and radicals.
• Mastering equations and inequalities.
• Understanding functions and their transformations.

To solve banking formulas such as \( Q = \frac{A-I}{L} \), intermediate algebra skills are critical. They allow you to:

• Identify and isolate variables through various mathematical operations.
• Manipulate and rearrange equations effectively.
• Develop problem-solving strategies that apply to diverse contexts, such as finance.

Building competency in intermediate algebra not only enhances your mathematical skills but also empowers you with tools for real-life applications.