Question

A mother explains to her child that the price on the sign is not the total price for a fancy watch, because the price does not include tax. She points out that a $790 fancy watch actually costs $869 once the sales tax is added. What is the sales tax percentage?

Write your answer using a percent sign (%).

Answer 1

Let \( P \) be the price of the watch before tax, which is $790. The total cost after adding sales tax can be represented as:

\[
\text{Total Cost} = P + \text{Tax}
\]

The tax can be calculated as:

\[
\text{Tax} = P \times \text{Sales Tax Percentage}
\]

Let \( r \) be the sales tax percentage expressed as a decimal. Therefore, our equation for the total cost becomes:

\[
\text{Total Cost} = P + (P \times r) = P(1 + r)
\]

Substituting the known values:

\[
869 = 790(1 + r)
\]

Next, we can isolate \( r \):

1. Divide both sides by 790:

\[
\frac{869}{790} = 1 + r
\]

2. Calculate \( \frac{869}{790} \):

\[
\frac{869}{790} \approx 1.100
\]

3. Now solve for \( r \):

\[
1 + r \approx 1.100
\]
\[
r \approx 1.100 - 1
\]
\[
r \approx 0.100
\]

4. Convert \( r \) to a percentage by multiplying by 100:

\[
\text{Sales Tax Percentage} = 0.100 \times 100 = 10\%
\]

Therefore, the sales tax percentage is

\[
\boxed{10\%}
\]