Problem 12 - Algebra 1: Concepts and Skills

Question

The price of a book without tax is $10. The sales tax rate on the price of the book is 6%. Solve the equation to find the amount of the tax.

Step-by-Step Solution

Answer

The sales tax on the book is $0.60.

Step 1: Write down what we know

We know that the pre-tax price of the book is $10 and that the sales tax rate is 6%. We need to find the amount of the tax. We can represent the tax rate of 6% as a decimal by dividing it by 100, to get 0.06.

Step 2: Apply the formula for calculating sales tax

The formula for calculating sales tax is: Sales Tax = Tax Rate × Pre-Tax Price. So, to find the sales tax, we multiply the pre-tax price of $10 by the tax rate of 0.06.

Step 3: Calculate the sales tax

Substituting the known values into the formula: Sales Tax = 0.06 × 10 = $0.60.

Key Concepts

Percentage Calculation

Percentage calculation is a fundamental mathematical skill used to determine a part of a whole. When given a percentage, you essentially want to find how much that percentage translates to in terms of quantity. In this context, we are converting the sales tax rate to a decimal form to use it in calculations.

To convert a percentage to a decimal, you divide it by 100. So, 6% becomes 0.06. This is necessary because mathematical operations in equations require numbers in decimal form rather than percentage.

Using percentages helps us understand fractions of 100, but converting them into decimals allows us to seamlessly perform calculations like multiplication or division.

Mathematical Operations

Mathematical operations are essential for solving equations, including those that involve percentages. In this case, the primary operation used is multiplication, as indicated by the formula:

• Sales Tax = Tax Rate × Pre-Tax Price

When multiplying, it is important to ensure that all unit conversions, such as converting a percentage to a decimal, have been made. This ensures the operation is correctly applied.

Here, you multiply the converted tax rate, 0.06, by the pre-tax price of the book, $10. This straightforward multiplication gives us the additional amount (the sales tax) that needs to be added to the pre-tax price to find the final cost.

Algebraic Expressions

Algebraic expressions allow us to represent real-world problems mathematically. They involve a combination of numbers, variables, and arithmetic operations. In the given exercise, the expression formed by the formula

• Sales Tax = Tax Rate × Pre-Tax Price

has no variables, only constants. Typically, such expressions would have variables representing unknown quantities.

However, even without variables, forming an expression still highlights how each component relates to others. Here, identifying the components (tax rate and pre-tax price) and setting them up in a multiplication operation helps us determine the sales tax seamlessly. Always remember to clearly define each part of your expression in the context of the problem.