Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Solve the equation R=r+400(W-L)/T for W
![### Solving the Equation
In this lesson, we will solve the given equation for \( W \). The equation is:
\[ R = r + \frac{400(W - L)}{T} \]
To isolate \( W \), we'll follow these steps:
1. **Subtract \( r \) from both sides**:
\[ R - r = \frac{400(W - L)}{T} \]
2. **Multiply both sides by \( T \) to eliminate the denominator**:
\[ T(R - r) = 400(W - L) \]
3. **Divide both sides by 400**:
\[ \frac{T(R - r)}{400} = W - L \]
4. **Add \( L \) to both sides to solve for \( W \)**:
\[ W = \frac{T(R - r)}{400} + L \]
So, the solution for \( W \) is:
\[ W = \frac{T(R - r)}{400} + L \]
This represents the steps to isolate \( W \) in the given equation. Now, \( W \) is expressed in terms of \( R \), \( r \), \( T \), and \( L \).
### Summary
Given the equation \( R = r + \frac{400(W - L)}{T} \), we solved for \( W \) and derived the formula:
\[ W = \frac{T(R - r)}{400} + L \]
Use these steps whenever you need to solve for \( W \) in a similar type of equation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5182fb9-e553-48f5-bc28-4c1fb0205165%2F2f9b15dd-b40f-4341-b47d-29052dc1e3fd%2F5bjrbt6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving the Equation
In this lesson, we will solve the given equation for \( W \). The equation is:
\[ R = r + \frac{400(W - L)}{T} \]
To isolate \( W \), we'll follow these steps:
1. **Subtract \( r \) from both sides**:
\[ R - r = \frac{400(W - L)}{T} \]
2. **Multiply both sides by \( T \) to eliminate the denominator**:
\[ T(R - r) = 400(W - L) \]
3. **Divide both sides by 400**:
\[ \frac{T(R - r)}{400} = W - L \]
4. **Add \( L \) to both sides to solve for \( W \)**:
\[ W = \frac{T(R - r)}{400} + L \]
So, the solution for \( W \) is:
\[ W = \frac{T(R - r)}{400} + L \]
This represents the steps to isolate \( W \) in the given equation. Now, \( W \) is expressed in terms of \( R \), \( r \), \( T \), and \( L \).
### Summary
Given the equation \( R = r + \frac{400(W - L)}{T} \), we solved for \( W \) and derived the formula:
\[ W = \frac{T(R - r)}{400} + L \]
Use these steps whenever you need to solve for \( W \) in a similar type of equation.
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