The after-tax cost of a certain item is $2,119. If the local tax rate is 1.6% and the state tax rate is 3.1%, find the sales tax of this item.

To find the sales tax on the item, we need to reverse-calculate based on the given after-tax cost and tax rates.

Let the original price of the item before taxes be denoted as $ P $.

The total tax rate is the sum of the local and state tax rates:

\[
\text{Total Tax Rate} = 1.6\% + 3.1\% = 4.7\% = 0.047
\]

The after-tax price is the original price plus the sales tax:

\[
\text{After-tax cost} = P + (\text{Total Tax Rate} \times P) = P(1 + 0.047)
\]

Given that the after-tax cost is $2,119, we can set up the following equation:

\[
P(1.047) = 2119
\]

Now, solve for $ P $:

\[
P = \frac{2119}{1.047} \approx 2024.07
\]

So, the original price of the item before taxes is approximately $2,024.07.

Now, to find the sales tax, subtract the original price from the after-tax cost:

\[
\text{Sales Tax} = 2119 - 2024.07 \approx 94.93
\]

Thus, the sales tax on the item is approximately **$94.93**.

Would you like more details on this calculation or any further clarification?

Here are 5 related questions you might consider:
1. How would the sales tax change if the local tax rate increased to 2%?
2. What would the original price be if only the state tax was applied?
3. How does the total tax rate compare to tax rates in neighboring states or regions?
4. If the after-tax cost were $2,500, what would the sales tax be with the same rates?
5. How can you calculate the total tax percentage directly from an after-tax amount?

**Tip**: Always break down percentages into decimal form for ease in calculations when solving for taxes or percentages.

The after-tax cost of a certain item is $2,119. If the local tax rate is 1.6% and the state tax rate is 3.1%, find the sales tax of this item.

Learn how to find the sales tax when the after-tax cost is $2,119 with local and state tax rates of 1.6% and 3.1%. This problem involves algebraic concepts and percentage calculations, suitable for students in Grades 9-12.

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