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Chapter 2: Problem 46

Express the amount of tax you pay on a car that costs \(c\) dollars at a tax rate of \(7 \% .\)

Short Answer

Expert verified
The tax is \(0.07c\) dollars.

Step by step solution

01

- Understand the problem

The problem requires finding the amount of tax paid on a car that costs \(c\) dollars with a tax rate of \(7\%\).
02

- Identify the formula to use

The amount of tax (T) can be calculated using the formula: \[ T = c \times \frac{7}{100} \]
03

- Substitute the values

Substitute the values into the formula: \[ T = c \times 0.07 \]
04

- Simplify the expression

Multiply the cost of the car (\(c\)) by \(0.07\) to find the tax amount.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Percentage Calculations
Understanding percentages is crucial when solving problems involving sales tax. A percentage represents a part per hundred. In this exercise, we're dealing with a 7% tax rate. This means that for every \(100 spent, you pay \)7 in tax. To convert a percentage to a decimal for calculations, divide by 100. Therefore, 7% becomes 0.07. You can use this conversion anytime you need to find a part of a whole.
Algebraic Expressions
An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations. In our problem, we use the expression \(T = c \times \frac{7}{100}\). Here, \(c\) is the cost of the car, and \(T\) represents the tax amount. Understanding how to write and interpret such expressions is key in solving problems.
Variable Substitution
Variable substitution involves replacing a variable in an expression with its actual value. For instance, in our formula \(T = c \times \frac{7}{100}\), if we know the actual cost of a car (say \(c = 20000\)), we substitute \(c\) with 20000. Our equation now becomes \(T = 20000 \times 0.07\). This step is essential for evaluating expressions and finding numerical answers.
Simplifying Expressions
Simplifying expressions makes them easier to work with. After substitution, our expression becomes \(T = 20000 \times 0.07\). Multiplying 20000 by 0.07 simplifies the problem to: \(T = 1400\). The tax amount is $1400. Simplifying helps in getting to the final answer quickly and accurately.

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