A rugby team scored 24 points, 17 points and 25 points in the seventh, eighth and ninth games of the 2022 season. Their average points-per-game was higher after 9 games than it was after their first 6 games. Their average after 10 games was more than 22. What is the smallest number of points that they could have scored in their 10th game? A 22 B 23 C 24 D 25 E 26
Question
A rugby team scored 24 points, 17 points and 25 points in the seventh, eighth and ninth games of the 2022 season. Their average points-per-game was higher after 9 games than it was after their first 6 games. Their average after 10 games was more than 22. What is the smallest number of points that they could have scored in their 10th game? A 22 B 23 C 24 D 25 E 26
Solution
To solve this problem, we first need to calculate the total points scored in the first 9 games. This is done by adding the points scored in the 7th, 8th, and 9th games:
24 points (7th game) + 17 points (8th game) + 25 points (9th game) = 66 points
We know that the average points-per-game after 9 games was higher than it was after the first 6 games. This means that the total points scored in the first 6 games must be less than 66 points.
We also know that the average after 10 games was more than 22 points. To find the minimum number of points that could have been scored in the 10th game, we can calculate the total points needed to have an average of 22 points after 10 games:
22 points/game * 10 games = 220 points
Subtract the total points scored in the first 9 games from this number to find the minimum number of points that could have been scored in the 10th game:
220 points - 66 points = 154 points
Therefore, the smallest number of points that they could have scored in their 10th game is 154 points. However, this number is not in the given options (A, B, C, D, E). There seems to be a mistake in the problem or the options provided.
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