a. \( c=w t+w \quad \) for \( t \)

To isolate \( t \) in the equation \( c = wt + w \), start by subtracting \( w \) from both sides: \( c - w = wt \). Next, divide both sides by \( w \) (assuming \( w \neq 0 \)): \( t = \frac{c - w}{w} \). Voilà! You've neatly solved for \( t \)! This equation can come in handy in fields like finance or physics where understanding the relationship between constants and variables can lead to more efficient problem solving. For example, if \( c \) represents total costs in a project (including fixed costs as \( w \)), you get insights into how time influences your variable costs, making budgeting much more straightforward!