To determine if Monica's estimate that she received about 50 points on average during each of the 3 rounds is reasonable, we first need to calculate the total number of points she earned during those rounds.
Monica started with –10 1/2 points and ended with 99 1/2 points.
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First, convert the mixed numbers to improper fractions:
- Starting points: \(-10 \frac{1}{2} = -\frac{21}{2}\)
- Ending points: \(99 \frac{1}{2} = \frac{199}{2}\)
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Calculate the total points she earned: \[ \text{Total points earned} = \text{Ending points} - \text{Starting points} \] \[ = \left(\frac{199}{2}\right) - \left(-\frac{21}{2}\right) \] \[ = \frac{199}{2} + \frac{21}{2} \] \[ = \frac{199 + 21}{2} = \frac{220}{2} = 110 \]
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Now, we can find the average points earned per round: \[ \text{Average points per round} = \frac{\text{Total points earned}}{\text{Number of rounds}} \] \[ = \frac{110}{3} \approx 36.67 \]
Monica estimates she received about 50 points on average during each of the 3 rounds. Since the calculated average is approximately 36.67 points, her estimate of 50 points is too high.
Therefore, Monica's estimate is not a good estimate.