Grades 7-8 Video Solutions 2023-2023_7-8

Video Transcription

Question 30. A rugby team scored 24 points, 17 points, and 25 points in the 7th, 8th, and 9th games of the 2022 season.  Their average of 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? First, let's find the average in the 7th, 8th, and 9th games.  For this, we will add the points, which equals 66, and divide by 3. So our average in the 7th, 8th, and 9th games is 22.  Assuming that they would have scored the same amount of points in each game for the first 6 games, multiply by 6 and get 132 points.  And we do know that the average of points per game was higher after 9 games than it was after the first 6. So this number 132 could not be. However, it could have been 131.  That is the most amount of points they could have gotten in the first 6 games. Next, let's assume that in all 10 games total, they scored an average of 22 points.  So they would have scored a total of 220 points. But we do know that the average after 10 games was more than 22. So, at minimum, they would have had to score 221 points.  So the smallest number of points that they could have scored in their 10th game will be 221 minus 131 minus 66, the number of points we know they scored.  When we do this math, we'll get our answer, which is 24. So the smallest number of points they could have scored will be C, 24.

Video Summary

To solve this problem, we first find that the rugby team's average score for the 7th, 8th, and 9th games was 22 points. For the first 6 games to have a lower average, they must have scored at most 131 points. For the average after 10 games to be more than 22 points, their total score must exceed 220 points. Therefore, their minimum requirement for the 10th game is calculated as 221 total points minus the 197 points already scored in the first 9 games, leading to a minimum of 24 points. Thus, the smallest number of points in the 10th game is 24.

Keywords

rugby team

average score

games

minimum points

calculation