Caleb paid \( \$ 27.10 \), including a \( 9 \% \) sales tax, for a security wallet. How much did the wallet itself cost?

To determine the cost of the security wallet before tax, let's break down the problem step by step. 1. **Understanding the Total Cost:** - The total amount Caleb paid is **\$27.10**, which includes a **9% sales tax**. 2. **Setting Up the Equation:** - Let \( x \) be the cost of the wallet before tax. - The total cost after including tax can be expressed as: \[ x + 0.09x = 1.09x = \$27.10 \] 3. **Solving for \( x \):** - To find the original price \( x \), divide the total amount by **1.09**: \[ x = \frac{27.10}{1.09} \] 4. **Calculating the Division:** - \( \frac{27.10}{1.09} \approx 24.862 \) 5. **Rounding to the Nearest Cent:** - The cost before tax is approximately **\$24.86**. 6. **Verification:** - To ensure accuracy, calculate the tax on \$24.86: \[ 24.86 \times 0.09 = 2.24 \] - Adding the tax to the original price: \[ 24.86 + 2.24 = 27.10 \] - This matches the total amount Caleb paid, confirming our solution. **Final Answer:** The security wallet cost **\$24.86** before tax.