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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 - no response given

0.1697%
0.1697% - no response given

17%
17% - no response given

14.5%

3 answers

To calculate the percent error, you can use the formula:

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

In this case, the expected value is $25,500 and the actual value is $21,800.

  1. Calculate the absolute error: \[ |\text{Expected Value} - \text{Actual Value}| = |25,500 - 21,800| = 3,700 \]

  2. Plug the values into the formula: \[ \text{Percent Error} = \frac{3,700}{25,500} \times 100 \]

  3. Calculate the fraction: \[ \frac{3,700}{25,500} \approx 0.1457 \]

  4. Multiply by 100 to get the percentage: \[ 0.1457 \times 100 \approx 14.57% \]

Rounding gives about 14.5%.

So the correct response is 14.5%.

The CORRECT ANSWER IS 17%

Apologies for any confusion earlier. Let's clarify the calculation for percent error once more given your assertion that the correct answer is 17%.

  1. Expected price of the truck: \( $25,500 \)
  2. Final negotiated price: \( $21,800 \)

We can calculate the error and then the percent decrease:

  1. Calculate the absolute error: \[ \text{Error} = \text{Expected Value} - \text{Actual Value} = 25,500 - 21,800 = 3,700 \]

  2. Calculate the percent error using the formula: \[ \text{Percent Error} = \frac{\text{Error}}{\text{Expected Value}} \times 100 \] \[ \text{Percent Error} = \frac{3,700}{25,500} \times 100 \approx 14.5% \]

Let's check if you were referring to the percentage reduction from the expected price rather than the percent error:

  1. To find the percentage decrease from the expected price: \[ \text{Percentage Decrease} = \frac{\text{Error}}{\text{Expected Price}} \times 100 \] \[ \text{Percentage Decrease} = \frac{3,700}{25,500} \times 100 \approx 14.5% \]

If you meant to calculate the amount saved as a percentage of the original expected price, then the calculation above is appropriate.

To summarize:

  • The correct percent error is approximately 14.5%.
  • If you were looking for 17%, please clarify how that value was derived or what the specific context was, as the calculations above reflect the percent error based on standard definition.

Thank you for your understanding!