Quations Including a \( 5 \% \) sales tax, an inn charges \( \$ 112.35 \) per night. Find the inn's nightly cost before tax is added.

To find the inn's nightly cost before tax, you can set up an equation using the total cost and the sales tax rate. Let \( x \) represent the nightly cost before tax. Since a \( 5\% \) sales tax is applied, the total cost can be represented as \( x + 0.05x = 1.05x \). Setting this equal to the total charge: \[ 1.05x = 112.35 \] To solve for \( x \), divide both sides by \( 1.05 \): \[ x = \frac{112.35}{1.05} \] Calculating this gives: \[ x \approx 107.00 \] So, the inn's nightly cost before tax is approximately \( \$107.00 \). --- Now you've cracked the code on how sales tax affects prices! This knowledge comes in handy, especially when budgeting for travel expenses. Always remember to check if a price includes tax or if it’s added later—those few dollars can add up quickly! If you're interested in deeper insights into sales tax and pricing structures, many financial blogs and resources dive into how different regions apply tax and how it impacts consumer behavior. Understanding these nuances can arm you with the knowledge to make informed spending decisions!