Question

Yu Yan planned to buy a new truck. She expected to pay $25,500. She negotiated the price so that the final cost was $21,800. Calculate the percent error. (1 point)
Responses

−17%
negative 17 percent

0.1697%
0.1697%

17%
17%

14.5%

Answer 1

To calculate the percent error based on Yu Yan's expected price and the negotiated price, we can use the following formula for percent error:

\[
\text{Percent Error} = \frac{\text{Actual Value} - \text{Expected Value}}{\text{Expected Value}} \times 100
\]

In this case:

- Actual Value = $21,800 (the negotiated price)
- Expected Value = $25,500 (the original expected price)

Now, substituting the values into the formula:

\[
\text{Percent Error} = \frac{21,800 - 25,500}{25,500} \times 100
\]

Calculating the numerator:

\[
21,800 - 25,500 = -3,700
\]

Now substitute that back into the formula:

\[
\text{Percent Error} = \frac{-3,700}{25,500} \times 100
\]

Calculating the fraction:

\[
\frac{-3,700}{25,500} \approx -0.1455
\]

Now multiply by 100 to convert to percentage:

\[
-0.1455 \times 100 \approx -14.55\%
\]

Rounding this value gives approximately:

\[
-14.5\%
\]

Therefore, the correct response is:

**−14.5%** (or -14.5 percent). If this was not listed and considering rounding and options provided, **14.5%** could also be an acceptable choice depending on context. Just make sure to clarify if a positive or negative sign is necessary.