Question Mary Ann played a game 5 times. Her scores for the first 4 times are shown: 72 84 72 81 Of the following scores, which could Mary Ann have gotten on her 5th game so the range of the scores was 257
The correct answer and explanation is:
To find the score Mary Ann could have gotten on her 5th game to achieve a range of 257, we need to first understand the range of a set of numbers. The range is the difference between the highest and lowest scores in the set. Given the scores from the first 4 games: 72, 84, 72, and 81, we can calculate the range of these scores.
- Find the highest and lowest scores in the first 4 games:
- Highest score: 84
- Lowest score: 72
- Calculate the current range:
Range = Highest score – Lowest score
Range = 84 – 72 = 12 - Determine the required range:
According to the question, the range of all 5 scores must be 257. So, we need to find a score for the 5th game such that the difference between the highest and lowest score in the set becomes 257. - Consider the possible outcomes for the 5th game:
- If the 5th score is lower than 72, it could potentially lower the range, but the range would still need to be 257.
- If the 5th score is higher than 84, it could increase the highest score, and thus increase the range.
- Calculate the required 5th score:
To get a range of 257, the difference between the highest score and the lowest score must be 257. Therefore:
- If the 5th score is higher than 84, the highest score would become this new score, and the lowest score (72) would remain the same.
- To achieve a range of 257, the new score must be:
$257 + 72 = 329$.
Thus, the score Mary Ann could have gotten on her 5th game to make the range 257 is 329.
Explanation: The range of a set of numbers is the difference between the highest and lowest values in the set. For Mary Ann’s scores to have a range of 257, the highest score must be 257 greater than the lowest score. Given that her lowest score is 72, the new highest score must be 329 to achieve the desired range of 257.