Question

A customer bought a clock for $$\$ 27.50$$, which included a \(10 \%\) sales tax. What was the price of the clock before tax? A) $$\$ 2.75$$ B) $$\$ 25.00$$ C) $$\$ 30.25$$ D) $$\$ 30.56$$ $$ \begin{array}{|c|c|} \hline \text { List } \mathrm{X} & \text { List } \mathrm{Y} \\ \hline 5 & 9 \\ \hline 8 & 10 \\ \hline 13 & 11 \\ \hline 13 & 15 \\ \hline 15 & 19 \\ \hline 18 & 20 \\ \hline \end{array} $$

Short answer

The original price of the clock before tax is \(\$25.00\), which is answer choice B.

Step-by-step solution

Identify the price paid including tax

The price paid for the clock, including tax, is given to be \$27.50.

Define the equation to determine pre-tax price

Let the original price of the clock be x. Price with tax can be calculated as the original price plus 10% of the original price. So, the equation will be: \[x + 0.10x = \$27.50\]

Simplify the equation

Combine the terms: \[1.10x = \$27.50\]

Solve for x

Divide both sides by 1.10 to get the value of x: \[x = \frac{\$27.50}{1.10}\]

Calculate the original price

Plug the given value in the equation to get the original price: \[x = \frac{\$27.50}{1.10} = \$25.00\]

Check answer and interpret result

The original price of the clock before tax is \$25.00, which is answer choice B.

Key concepts

Sales Tax Calculation

Sales tax is an additional charge placed on goods or services, usually as a percentage of the original price. For instance, when a customer purchases an item, they often pay more than the base price due to this added tax. Understanding how to calculate sales tax can clarify how much you're truly paying. In this exercise, the price of a clock the customer paid includes a 10% sales tax.

• The total amount paid is $27.50, encompassing both the clock's original price and the sales tax.
• To find the clock's original price, you need to "reverse-calculate" the effect of a 10% tax increment.
• Remember, sales tax can significantly affect the final purchase price, which is why it is crucial to understand it in financial math.

By calculating backward, knowing the total price and the tax rate, you can determine the initial price of the product before the sales tax was applied.

Algebraic Equations

Algebraic equations are mathematical statements that express equality between two expressions and involve variables. They are powerful tools to solve problems involving unknowns. In this clock problem, we use an algebraic equation to determine the original price before tax.

• Define the unknown: Let the original price be represented by the variable \(x\).
• Form the equation: Including tax, the total price is expressed as \(x + 0.10x = 27.50\).
• Simplify the equation: Combine like terms to get \(1.10x = 27.50\).

Equations allow us to perform logical operations to isolate the unknown variable and find its value. Solving equations involves operations like addition, subtraction, multiplication, or division to keep both sides equal and determine the unknown.

Percentages in Math

Percentages are a way to express numbers as a fraction of 100. This means it can describe parts of a whole, making them extremely useful in various math applications, such as calculating sales tax.

• To find 10% of the original price \(x\), multiply \(x\) by 0.10.
• Percentages simplify the comparison and calculation of proportions over a standardized base of 100.
• In this problem, you understand percentages by noting that 10% sales tax increases an original cost by one tenth.

Understanding percentages enables you to tackle calculations of discounts, interest rates, and other financial computations in everyday life. In essence, percentages bridge the gap between fractions, decimals, and real-world problems.