Problem 18 - Algebra and Trigonometry

Question

Including \(5 \%\) sales tax, an inn charges \(\$ 252\) per night. Find the inn's nightly cost before the tax is added.

Step-by-Step Solution

Answer

To find the pre-tax cost, we divide the total cost by 1.05. The pre-tax nightly cost of the inn is \(252/1.05 = \$240\).

Step 1: Understand the relationship between pre-tax cost and post-tax cost

If the pre-tax cost is \(x\), then adding 5% sales tax to it would make the cost as \(x + 0.05x = 1.05x\). We are given that \(1.05x = 252\).

Step 2: Compute the pre-tax cost

To find the pre-tax cost, \(x\), we need to rearrange and solve the equation. Dividing the entire equation by 1.05, we get \(x = 252/1.05\)

Step 3: Solve the equation

By carrying out the division above, we can obtain the pre-tax cost.