Question

Andy estimated that he would need 73 feet of lumber for a tree house project. He later found that the actual amount of lumber needed was 62 feet. What was the percent error of Andy's estimation?

Answer 1

To calculate the percent error of Andy's estimation, we can use the formula for percent error:

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

In this case, the estimated value is 73 feet and the actual value is 62 feet.

First, find the absolute error:

\[
|\text{Estimated Value} - \text{Actual Value}| = |73 - 62| = 11 \text{ feet}
\]

Next, calculate the percent error:

\[
\text{Percent Error} = \left( \frac{11}{62} \right) \times 100\%
\]

Calculating the fraction:

\[
\frac{11}{62} \approx 0.1774
\]

Now, multiply by 100 to convert it to a percentage:

\[
0.1774 \times 100\% \approx 17.74\%
\]

Thus, the percent error of Andy's estimation is approximately

\[
\boxed{17.74\%}
\]