LEAVING A TIP In Exercises 83-85, use the following...

LEAVING A TIP In Exercises $83-85$, use the following information. You and a friend decide to leave a $15 \%$ tip for restaurant service. You compute the tip, $T,$ as $T=0.15 C,$ where $C$ represents the cost of the meal. Your friend claims that an easier way to mentally compute the tip is to calculate $10 \%$ of the cost of the meal plus one half of $10 \%$ of the cost of the meal. Write an equation that represents your friend's method of computing the tip.

LEAVING A TIP In Exercises $83-85$, use the following information. You and a friend decide to leave a $15 \%$ tip for restaurant service. You compute the tip, $T,$ as $T=0.15 C,$ where $C$ represents the cost of the meal. Your friend claims that an easier way to mentally compute the tip is to calculate $10 \%$ of the cost of the meal plus one half of $10 \%$ of the cost of the meal.
Write an equation that represents your friend's method of computing the tip.

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Key Concepts

Equation Formulation

Equation formulation refers to the process of translating a word problem into a mathematical equation. This includes identifying the components of the problem, such as percentages and costs, and accurately representing the given relationships with an appropriate algebraic expression.

Percentage Calculation

Percentage calculation involves converting a given percentage into a decimal form and then multiplying by the whole. For instance, finding 15% of a number requires multiplying the number by 0.15. This concept is essential in various applications from financial calculations to probability.

Algebraic Representation

Algebraic representation is the use of variables and equations to express mathematical concepts and relationships. In problems involving percentages, it allows for the formulaic expression of quantities, making it easier to generalize and solve the problem systematically.

Mental Computation Techniques

Mental computation techniques simplify arithmetic operations by breaking down complex percentages into smaller, more manageable parts. For example, computing 15% by adding 10% plus half of 10% (which equals 5%) leverages the ease of working with round numbers to achieve the same result as a single multiplication.

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