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Chapter 6: Problem 41

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

Short Answer

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

Step by step solution

01

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.
02

Multiply by L to Eliminate the Denominator

To eliminate the fraction, multiply both sides of the equation by \( L \). This gives \( QL = A - I \).
03

Isolate A

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

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Key Concepts

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

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.

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Most popular questions from this chapter

Solve equation. If a solution is extraneous, so indicate. \(\frac{-5}{c+2}=\frac{3}{2-c}+\frac{2 c}{c^{2}-4}\)

Use synthetic division to perform each division. $$ \frac{-6 c^{5}+14 c^{4}+38 c^{3}+4 c^{2}+25 c-36}{c-4} $$

Use synthetic division to perform each division. $$ \frac{2 x^{3}+3 x^{2}-8 x+3}{x+3} $$

For each expression in part (a), perform the indicated operations and then simplify, if possible. Solve equation in part (b) and check the result. a. \(\frac{a^{2}+1}{a^{2}-a}-\frac{a}{a-1}\) b. \(\frac{a^{2}+1}{a^{2}-a}-\frac{a}{a-1}=\frac{1}{a}\)

Use the factor theorem and determine whether the first expression is a factor of \(P(x) .\) See Example 5. $$ x-3 ; P(x)=x^{3}-3 x^{2}+5 x-15 $$
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