Question

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. Simplify the equation. What property did you use to simplify the equation?

Short answer

The equation simplifies to \(T = 0.15C\) which is equivalent to the tip calculation used originally. The mathematical properties used to simplify the equation include the Distributive Property and Arithmetic operations to combine like terms.

Step-by-step solution

Setup the Equation

Start by expressing the 'Easier Method' for calculating the tip mentioned by your friend i.e., \(10 \%\) of the cost of the meal + \(\frac{1}{2}\) of \(10 \%\) of the cost of the meal. Take \(C\) to be the cost of the meal. Hence, the equation becomes: \(T = 0.10C + 0.5 \cdot 0.10C \)

Simplify the Equation

Use the Distributive property of multiplication over addition to simplify the equation: \(T = 0.10C + 0.05C\)

Combine Like Terms

The like terms - the terms with the same variable, to the same power can be combined to simplify the equation further. This gives us: \(T = 0.15C\)

Identify the property

The properties which we applied in this problem are 'Distributive Property' to distribute 0.5 over 0.10C and then 'Combination of Like terms' which is part of Arithmetic operations to combine 0.10C and 0.05C.