Problem 37 - Elementary Algebra Within Reach

Question

The sales tax on a purchase of \(L\) dollars is \(6 \%\). Write an algebraic expression that represents the total amount of sales tax. (Hint: Use the decimal form of \(6 \%\).)

Step-by-Step Solution

Answer

The algebraic expression that represents the total amount of sales tax is \(0.06L\).

Step 1: Convert Percentage to Decimal

First, convert the percentage to a decimal value, so 6% is equivalent to 0.06 as a decimal. This is done by dividing 6 by 100.

Step 2: Formulate the equation

Given that the cost of the purchase (before tax) is L dollars, the total sales tax can be found by multiplying the cost of the purchase (L) by the tax rate (0.06). The algebraic expression is \(0.06L\).

Key Concepts

Sales Tax Calculation

Understanding sales tax calculation is crucial, as it's a common real-life application of algebra that affects everyday purchases. Basically, sales tax is a percentage of the item's cost that is added on by the government as a part of the total price. To calculate the amount of sales tax, you multiply the cost of the item by the sales tax rate.

For example, if you purchase a book for \(50 and the sales tax rate is 8%, the sales tax you would pay is \)4 (which is 8% of $50). However, to perform this multiplication, you need to convert the percentage into decimal form, which is a simpler format for computation in algebra. Once the sales tax is calculated, it is added to the original price to determine the final cost of the item. Sound knowledge of this concept not only helps you in understanding algebra but also prepares you for managing finances in daily life.

Percentage to Decimal Conversion

Conversion from percentage to decimal is an essential skill in solving many algebraic problems, including sales tax calculations. The percentage represents a fraction of 100, so to convert a percentage to a decimal, you simply divide by 100.

Here's a quick guide on how to do this:

• Place the percentage number over 100 (e.g., 6% becomes 6/100).
• Divide the top number by the bottom number (e.g., 6 ÷ 100 = 0.06).
• The result is the decimal equivalent of the percentage.

Such conversion is necessary because algebra commonly deals with numbers in decimal form as it simplifies multiplication, division, and other operations. When you work with percentages directly in equations, conversion to decimals will make your computations much more straightforward.

Writing Algebraic Equations

Writing algebraic equations is a fundamental component of algebra that translates real-world situations into mathematical statements. It involves representing relationships between quantities with symbols and variables.

An algebraic equation can include numbers, variables (letters that represent unknown values), and operation signs. The equation is a way of stating that two expressions are equal. To write one effectively, follow these steps:

• Identify the variables and constants involved.
• Translate the verbal description of the problem into an equation using algebraic symbols.
• Ensure that the equation logically represents the situation described in the problem.

The ability to write algebraic equations is powerful; it allows you to solve problems ranging from simple arithmetic to complex real-world scenarios. By practicing this skill, you develop the ability to think critically and abstractly about numbers and their relationships.