Problem 25 - Prealgebra

Question

The following problems are similar to Problems \(1-22\). Set them up in the same way, but use a calculator for the calculations. Tax Rate The purchase price for a new suit is $$ 229.50 .\( If the sales tax is $$ 10.33,\) what is the sales tax rate? (Round to the nearest tenth of a percent.)

Step-by-Step Solution

Answer

The sales tax rate is approximately 4.5%.

Step 1: Understand the Problem

We are given the purchase price of a suit at $229.50 and the sales tax of $10.33. We need to find the sales tax rate as a percentage of the purchase price.

Step 2: Use the Sales Tax Formula

The sales tax rate can be calculated using the formula: \[\text{Sales Tax Rate} = \left( \frac{\text{Sales Tax}}{\text{Purchase Price}} \right) \times 100\] Substitute \(10.33 for sales tax and \)229.50 for purchase price.

Step 3: Plug in the Values

Substitute the given values into the formula: \[\text{Sales Tax Rate} = \left( \frac{10.33}{229.50} \right) \times 100\]

Step 4: Calculate the Fraction

Calculate the fraction: \[\frac{10.33}{229.50} \approx 0.044998\]

Step 5: Convert to Percentage

Convert the fraction to a percentage by multiplying by 100: \[0.044998 \times 100 = 4.4998\]

Step 6: Round the Result

Round the result to the nearest tenth: The sales tax rate is approximately 4.5%.

Key Concepts

Percentage Calculation

When we talk about percentages, we are referring to a part out of one hundred. It's a way of expressing a number as a fraction of 100, and is often denoted using the symbol \(%\). To convert a fraction or a decimal to a percentage, we multiply by 100. For example, if you have a decimal like 0.5, converting to a percentage involves the calculation: \(0.5 \times 100 = 50\%\).
Percentage calculations are widely used in various scenarios like calculating discounts, interest rates, and yes, sales tax too! To tackle any percentage problem, you generally would recognize a part-whole relationship; the 'part' refers to the known value, and the 'whole' to the total situation. Understanding this will let you set up the equation needed to solve your problem effectively.

Prealgebra Problems

Prealgebra forms the foundation for tackling more complex math problems. It involves basic arithmetic operations—addition, subtraction, multiplication, and division—and introduces variables, fractions, decimals, and basic equations.
In the context of calculating sales tax, prealgebra comes into play as you are working with decimals and fractions. Consider the exercise given: you have a price of \(229.50 and a sales tax of \)10.33. Prealgebra helps you understand that you can use division to find what percentage of the price the tax represents. You'll deal with fractions like \(\frac{10.33}{229.50}\), where understanding how to manage decimals and fractions becomes essential. This basic math competency is necessary as a precursor to more advanced topics like algebra.

Sales Tax Formula

To calculate sales tax, it's essential to understand the sales tax formula. This formula lets you determine the percentage of the purchase cost that constitutes the tax. One common formula used is:\[\text{Sales Tax Rate} = \left( \frac{\text{Sales Tax}}{\text{Purchase Price}} \right) \times 100\]In this formula, you divide the sales tax by the purchase price to find the fraction the tax represents of the total purchase cost. Multiplying this fraction by 100 converts it into a percentage, providing the sales tax rate. In our exercise, applying this formula required substituting the given values of sales tax (\(10.33) and purchase price (\)229.50) into the equation. First, you calculate \(\frac{10.33}{229.50}\), which gives a decimal. Then, you convert it into a percentage by multiplying by 100, resulting in 4.4998%. Rounding to the nearest tenth, the final answer is approximately 4.5%. This formula simplifies determining how much tax is being paid relative to the purchase price, making it a practical tool for real-life shopping scenarios.