Last year, Theodora estimated that she would sell 96 bracelets. But at the end of the year, she had 16 bracelets left over. Which explains how Theodora can find the percent error of her estimate?

Question

First, find that the exact value is 96 minus 16 = 80. The error is 16. The absolute error is 16. Set up the ratio with the absolute error: StartFraction 16 over 80 EndFraction. Divide and then multiply by 100 to find the percent error: (0.20) (100) = 20 percent.
First, find that the exact value is 96 minus 16 = 80. The error is 16. The absolute error is 16. Set up the ratio with the absolute error: StartFraction 16 over 96 EndFraction. Divide and then multiply by 100 to find the percent error: (0.166) (100) = 16.7 percent.
First, find that the exact value is 96 +16 = 112. The error is 16. The absolute error is 16. Set up the ratio with the absolute error: StartFraction 16 over 112 EndFraction. Divide and then multiply by 100 to find the percent error: (0.14286) (100) = 14.3 percent.
First, find that the exact value is 96 + 16 = 112. The error is 16. The absolute error is 32. Set up the ratio with the absolute error: StartFraction 32 over 112 EndFraction. Divide and then multiply by 100 to find the percent error: (0.285) (100) = 28.5 percent.

Answer 1

To correctly calculate the percent error of Theodora's estimate, we first need to clarify how percent error is defined. Percent error can be calculated using the formula:

\[ \text{Percent Error} = \left( \frac{\text{Absolute Error}}{\text{True Value}} \right) \times 100 \]

In this context:

1. The estimated value is 96 bracelets.
2. The actual value (or "true value") is 80 bracelets, which is calculated by subtracting the 16 unsold bracelets from her estimate (96 - 16 = 80).

Now, we calculate the absolute error:

• Absolute Error = Estimated Value - Actual Value = 96 - 80 = 16.

Next, we can set up the ratio for the percent error using the actual value (80):

\[ \text{Percent Error} = \left( \frac{16}{80} \right) \times 100 = 0.20 \times 100 = 20% \]

So, the correct setup for calculating the percent error using the absolute error of 16 relative to her actual sales of 80 is as follows:

• First, find the exact value: 96 - 16 = 80.
• The error is 16. The absolute error is 16.
• Set up the ratio with the absolute error: \(\frac{16}{80}\).
• Divide and then multiply by 100 to find the percent error: \(0.20 \times 100 = 20%\).

The first option correctly explains how Theodora can find the percent error of her estimate.