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Chapter 2: Problem 28

Solve for the specified variable. \(A=P+P r t\) for \(r\)

Short Answer

Expert verified
\(r = \frac{A - P}{Pt}\)

Step by step solution

01

- Isolate the term containing r

Start by isolating the term that contains the variable r. The equation is given by: A = P + PrtSubtract P from both sides to isolate the Prt term: A - P = Prt
02

- Solve for r

To solve for r, divide both sides of the equation by Pt: \(\frac{A - P}{Pt} = r\)

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Key Concepts

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

Isolate Terms
Isolating terms is the first step in solving an equation for a specific variable. When we isolate a term, we aim to get the term with the variable we want to solve for on one side of the equation. This makes it easier to manipulate and solve.

For example, in the equation given: \(A=P+P r t\), our goal is to solve for \(r\). First, we need to isolate the term that contains \(r\), which is \(P r t\). To do this, we subtract \(P\) from both sides of the equation:

\[ A - P = Prt \]

This effectively moves all terms without \(r\) to the other side, isolating our term of interest.
Algebraic Manipulation
Once we have isolated the term containing the variable we want, we use algebraic manipulation to further simplify and solve the equation. Algebraic manipulation involves applying mathematical operations like addition, subtraction, multiplication, and division to both sides of an equation to maintain equality.

In our example, after isolating \(Prt\), we need to solve for \(r\). This requires dividing both sides of the equation by \(Pt\):

\[ \frac{A - P}{Pt} = r \]

By performing this division, we isolate \(r\) on one side of the equation. Remember to perform the same operation to each side to keep the equation balanced.
Equation Solving
Equation solving is the process of finding the value of a variable that makes the equation true. It often involves a combination of isolating terms and algebraic manipulation.

In our case, once we have performed the necessary isolations and manipulations, we reach the final equation:

\[ r = \frac{A - P}{Pt} \]

This tells us that, for any given values of \(A\), \(P\), and \(t\), we can find the value of \(r\) by substituting them into this equation. As shown, solving an equation step-by-step helps break down the problem and makes the process clear and manageable for any variable we need to solve for.

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Most popular questions from this chapter

Solve each problem. The area of a trapezoid is 200 square centimeters. The bases are 16 centimeters and 24 centimeters. Find the height.

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