Solve. Bridgewater Legal Offices charges a 250 retainer fee...

Solve.
Bridgewater Legal Offices charges a $\$ 250$ retainer fee for real estate transactions plus $\$ 180$ per hour. Dockside Legal charges a $\$ 100$ retainer fee plus $\$ 230$ per hour. For what number of hours does Bridgewater charge more?

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Key Concepts

Inequality Solving

When comparing two linear cost functions, an inequality can be set up to determine for what values of the variable one cost exceeds the other. This process involves writing an inequality, isolating the variable, and solving for the point where one service becomes more expensive than the other.

Linear Cost Functions

This concept involves representing costs with equations that include a fixed component (such as a retainer fee) and a variable component (an hourly rate). The overall cost is expressed as a linear function of the number of hours worked, which makes it straightforward to compare different services by examining the slope and intercept of the lines.

Break-even Analysis

Break-even analysis in this context involves finding the value of the variable (in this case, the number of hours) at which the costs of two services are equal. Understanding this concept allows one to determine the threshold beyond which one service becomes costlier, thereby aiding in comparing pricing structures.

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