Problem 91 - College Algebra Essentials

Question

$$\text { Solve for } C: \quad V=C-\frac{C-S}{L} N$$

Step-by-Step Solution

Answer

The solution for 'C' is given by the formula \( C = \frac{V - \frac{S \cdot N}{L}}{1 - \frac{N}{L}} \).

Step 1: Identify the problem

The main goal is to solve the equation for 'C'. The equation given is \( V = C - \frac{C - S}{L} \cdot N \). This equation needs to be rewritten with 'C' isolated.

Step 2: Expand the equation

Firstly, distribute 'N' in the parentheses by multiplying it with each term in the fraction yielding: \( V = C - N \cdot (\frac{C}{L} - \frac{S}{L}) \). Then convert into a more standard polynomial form: \( V = C - \frac{C \cdot N}{L} + \frac{S \cdot N}{L} \).

Step 3: Group 'C' terms together

Reorder the terms of the equation to gather 'C' terms together resulting in: \( V - \frac{S \cdot N}{L} = C - \frac{C \cdot N}{L} \).

Step 4: Factor 'C'

Now, factor out 'C' from the right side will give: \( V - \frac{S \cdot N}{L} = C \cdot (1 - \frac{N}{L}) \).

Step 5: Solve for 'C'

Lastly, divide both sides by (1 - \(\frac{N}{L}\)) to isolate 'C': \( C = \frac{V - \frac{S \cdot N}{L}}{1 - \frac{N}{L}} \).