Question

Including a 8 % sales​ tax, an inn charges $ 172.80 per night. Find the​ inn's nightly cost before tax is added.
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Part 1
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Answer 1

To find the inn's nightly cost before tax is added, you can use the following formula:

\[
\text{Cost before tax} = \frac{\text{Total cost}}{1 + \text{Sales tax rate}}
\]

Given:
- Total cost (including tax) = $172.80
- Sales tax rate = 8% = 0.08

Now, plug the values into the formula:

\[
\text{Cost before tax} = \frac{172.80}{1 + 0.08} = \frac{172.80}{1.08}
\]

Now, calculate it:

\[
\text{Cost before tax} = \frac{172.80}{1.08} \approx 160.00
\]

Thus, the inn's nightly cost before tax is approximately **$160.00**.