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Chapter 2: Problem 30

Solve each formula for the indicated letter. $$ P=\frac{a b}{c}, \text { for } b $$

Short Answer

Expert verified
The formula solved for b is $$ b = \frac{P \cdot c}{a} $$

Step by step solution

01

Understand the Formula

The given formula is $$ P = \frac{a b}{c} $$ which means that P is the result of dividing the product of a and b by c. The goal is to solve for the variable b.
02

Isolate the Denominator

Firstly, multiply both sides of the equation by c to eliminate the fraction: $$ P \cdot c = a b $$
03

Solve for b

Now, divide both sides of the equation by a to isolate b: $$ b = \frac{P \cdot c}{a} $$

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Key Concepts

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

Algebraic Manipulation
In algebra, manipulating equations is key to solving problems. You start with an equation involving variables and constants, and need to perform various mathematical operations to isolate a particular variable.
  • Addition or subtraction
  • Multiplication or division
  • Using properties of equality

For instance, in the given exercise, we wanted to solve for the variable b in the formula \( P = \frac{a b}{c} \).
Algebraic manipulation helps in changing the form of this equation step-by-step to achieve the solution.
Formula Rearrangement
Rearranging a formula means rewriting it so that a particular variable is isolated on one side. This is essential when you need to solve for a specific variable within an equation.

In the given problem, the formula was \( P = \frac{a b}{c} \) and we needed to isolate b.
  • The first step was to eliminate any fractions: Multiply both sides by \( c \).
    Result: \( P \cdot c = a b \).
  • After clearing the fraction, you divide both sides by \( a \) to isolate b.
    Final Result: \( b = \frac{P \cdot c}{a} \).

By rearranging the formula, you can express the variable you are solving for in terms of the other variables.
Isolate Variable
Isolating a variable means getting that variable alone on one side of the equation. Here, we wanted to isolate b in the formula \( P = \frac{a b}{c} \).
  • First step involved multiplying by c to get rid of the fraction.
    We achieved: \( P \cdot c = a b \).
  • Next, we divided by a to ensure b is by itself.
    The isolated variable solution: \( b = \frac{P \cdot c}{a} \).

Isolating variables is a foundational skill in algebra. Remember to apply equal operations on both sides of the equation.
This ensures the integrity of the equation while isolating the desired variable.

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Most popular questions from this chapter

Use an inequality and the five-step process to solve each problem. Reduced Fat Oreo " cookies contain 4.5 of fat per serving. In order for a food to be labeled "reduced fat," it must have at least \(25 \%\) less fat than the regular item. What can you conclude about the number of grams of fat in a serving of the regular Oreo cookies?

To prepare for Section \(2.6,\) review inequalities. Write a second inequality with the same meaning. $$x \geq-4$$

Translate to an inequality. The maximum safe-exposure limit of formaldehyde is 2 parts per million.

To prepare for Section 2.5, review translating to algebraic expressions and equations. Translate to an algebraic expression or equation. 10 more than three times a number

Match the sentence with one of the following: $$ a
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