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.

Answer 1

To calculate the percent error in Yu Yan's truck purchase, we can use the following formula for percent error:

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

In this case:
- Expected Value = 25,500
- Actual Value = 21,800

Now, we can plug in the values:

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

Calculating the difference:

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

Now, substituting this back into the percent error formula:

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

Calculating the fraction:

\[
\frac{-3,700}{25,500} \approx -0.1457
\]

Now multiply by 100 to convert to a percentage:

\[
\text{Percent Error} \approx -0.1457 \times 100 \approx -14.57
\]

Since percent error is expressed as a positive value, we take the absolute value:

\[
\text{Percent Error} \approx 14.57\%
\]

Thus, the percent error is approximately **14.57%**.