At a restaurant, if a party has eight or more people, the...

At a restaurant, if a party has eight or more people, the gratuity is automatically added to the bill. If $x$ is the cost of the meal, then the total bill $C(x)$ with an $18 \%$ gratuity and a $6 \%$ sales tax is given by: $C(x)=x+$ $0.06 x+0.18 x$. Evaluate $C(225)$ and interpret the meaning in the context of this problem.

Key Concepts

Percentage Calculation

This key concept involves understanding how to adjust a base value by a given percentage. In many real-world applications such as billing, tax, or gratuity calculations, percentages are used to determine an added amount relative to the original value. Here, calculating 6% sales tax and 18% gratuity involves multiplying the base cost by the respective percentage expressed as a decimal.

Algebraic Function Formation

An algebraic function is used to represent the relationship between the base cost and the total bill. In this context, the function C(x) = x + 0.06x + 0.18x represents the process of adding both the sales tax and the gratuity to the original meal cost. The formation of this function provides a methodical way to calculate increased totals using basic algebraic operations.

Function Evaluation

This concept involves computing the value of the function for a specific input. By substituting a particular cost (such as $225) into the function C(x), one can determine the resulting total bill. Function evaluation is essential in applying abstract mathematical expressions to real-world figures, ensuring the accuracy of practical calculations.

Interpretation in Context

Interpretation in context is the practice of relating a mathematical result back to the real-world scenario from which the problem arises. Once the function is evaluated, understanding that the computed total (for example, $279 for a $225 meal) includes both the applicable sales tax and the mandatory gratuity enables individuals to make informed decisions based on their financial obligations.

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