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Chapter 5: Problem 73

Solve each equation for the specified variable. $$ A=P+P r t \text { for } P $$

Short Answer

Expert verified
P = \frac{A}{1 + rt}

Step by step solution

01

Identify the equation

The given equation is: \[A = P + Prt\]The objective is to solve for the variable \(P\).
02

Factor out \(P\)

Notice that \(P\) is a common factor in the terms on the right-hand side. Factor \(P\) out of the terms involving \(P\):\[A = P(1 + rt)\]
03

Isolate \(P\)

To solve for \(P\), divide both sides of the equation by \(1 + rt\): \[P = \frac{A}{1 + rt}\]

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Key Concepts

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

Factoring
Factoring is a key skill in algebra. It means rewriting an expression by finding a common factor and simplifying the expression.
In the given problem, our goal is to solve the equation \(\text{A = P + Prt}\) for \(P\).
Notice that \(P\) is present in both terms on the right side of the equation. By factoring \(P\) out, we make the equation simpler to handle.
So, we rewrite \(P + Prt\) as \(P(1 + rt)\). This lets us easily isolate \(P\), making solving much easier.
Isolating Variables
Isolating the variable means rearranging the equation so that the variable you need to solve for is on one side of the equation, and everything else is on the other.
In our exercise, after factoring out \(P\), we have the equation \(\text{A = P(1 + rt)}\). Now we need to get \(P\) alone on one side.
To isolate \(P\), divide both sides of the equation by \(1 + rt\). This means we now have: \[P = \frac{A}{1 + rt}\]
Now, \(P\) is isolated, and we have our final answer.
Algebraic Manipulation
Algebraic manipulation involves the use of various techniques to transform an equation into a desired form.
This can include adding, subtracting, multiplying, or dividing both sides of the equation by the same value, factoring, expanding, and combining like terms.
In our problem, we used these skills by factoring out \(P\) and then dividing both sides by \(1 + rt\) to solve for \(P\).
Mastering these tools will help you to solve even more complicated equations later on.

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Most popular questions from this chapter

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