To determine the cost of the jacket before tax, we need to work through the following steps:
1. Understand the total cost and the tax rate:
- The total cost of the jacket, including tax, is [tex]$79.49.
- The sales tax rate is 6%.
2. Convert the tax rate to its decimal form:
- A 6% tax rate can be expressed as \( \frac{6}{100} = 0.06 \).
3. Set up the equation:
- Let \( x \) represent the cost of the jacket before tax.
- Adding a 6% tax to the cost of the jacket gives: \( x + 0.06x = 79.49 \).
4. Simplify the equation:
- Combine like terms: \( x \times (1 + 0.06) = 79.49 \).
- This simplifies to \( 1.06x = 79.49 \).
5. Solve for \( x \):
- To isolate \( x \), divide both sides of the equation by 1.06:
\[
x = \frac{79.49}{1.06}
\]
6. Calculate the value of \( x \):
- Performing the division gives:
\[
x \approx 74.99056603773585
\]
Therefore, the cost of the jacket before the tax is approximately $[/tex]74.99 (to two decimal places).
