A customer paid 53.00 for a jacket after a 6 percent sales...

A customer paid $\$ 53.00$ for a jacket after a 6 percent sales tax was added. What was the price of the jacket before the sales tax was added? \begin{equation} \begin{array}{l}{\text { A) } \$ 47.60} \\ {\text { B) } \$ 50.00} \\ {\text { C) } \$ 52.60} \\ {\text { D) } \$ 52.84}\end{array} \end{equation}

A customer paid $\$ 53.00$ for a jacket after a 6 percent
sales tax was added. What was the price of the jacket
before the sales tax was added?
\begin{equation}
\begin{array}{l}{\text { A) } \$ 47.60} \\ {\text { B) } \$ 50.00} \\ {\text { C) } \$ 52.60} \\ {\text { D) } \$ 52.84}\end{array}
\end{equation}

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Key Concepts

Percentage Increase

This concept involves determining a new amount by adding a certain percentage to the original value. In many applications, including taxes and discounts, the final amount is a percentage greater (or lesser) than the original, and understanding how to calculate this increase is fundamental to solving such problems.

Reverse Percentage Calculation

This involves finding the original value before a percentage increase or decrease was applied. It requires reversing the operation, typically by dividing the final amount by one plus (or minus) the percentage expressed as a decimal. This method is crucial when the final amount after an increase, such as tax, is known and the original amount needs to be determined.

Algebraic Equation Setup and Solving

In many percentage problems, setting up an equation that relates the known final amount to the unknown original amount is necessary. This involves using variables to represent unknown quantities and applying fundamental algebraic operations to isolate and solve for these variables. This process is a key tool in translating real-world percentage problems into mathematical form.

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