Question

Teachers at Price Middle School are planning a birthday party for the principal. Planners estimated that 42 slices of cake would be needed. In fact, only 30 slices of cake were eaten. What was the percent error in the estimate of how much cake was eaten?

A student solved the problem and showed his work below. What was his error?

|42-30|
---------- (100) = 6%
42
1. The planners did not use the absolute error in the ratio.
2. The planners compared the absolute error to the approximate value.
3. The planners did not multiply by 100 to get the percent.
4. The planners divided incorrectly and got the wrong answer.

Answer 1

The correct percent error is 40%, not 6%. The error in the student's work was using the estimated value instead of the true value in the calculation. The student should have used the true value (30 slices) for the calculation of percent error.

Step-by-step explanation:

The question is about calculating percent error in an estimation. It involves the steps of finding the absolute error, taking the ratio of the absolute error to the true value, and converting that into a percentage. The student's provided work shows an error in the step of taking the ratio. Let's correct the calculation:

To find the percent error, you do the following steps:

1. Calculate the absolute error: |42 - 30| = 12 slices.
2. Divide the absolute error by the true value: 12 / 30.
3. Multiply the result from step 2 by 100 to get the percentage: (12 / 30) * 100 = 40%.

The correct percent error is 40%, not 6%. The student's error was in dividing by the estimated value (42 slices) instead of the true value (30 slices). Therefore, the correct selection in response to the student's work is option 2: The planners compared the absolute error to the approximate value.