After a week-long sports tournament, Tara and Emek were asked to prepare a report comparing teams that had played different numbers of matches. They realized that total wins and total points alone would not provide a fair comparison. Instead, they calculated ratios such as points scored per match and win percentage, allowing every team to be evaluated on the same basis. One team had fewer total points but a higher average points per match than teams that had played more games. By interpreting these ratios rather than absolute totals, Tara and Emek produced a fair performance analysis, helping the organizers recognize the strongest overall team.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Divide each team's total points by its number of matches.
Team A scored 84 points in 6 matches. Team B scored 100 points in 8 matches. Which statement correctly compares their average points per match?
The teams had the same average because both scored more than 80 points.Team B had the higher average, with 12.5 points per match.Team A had the higher average, with 14 points per match.Team B had the higher average because it scored more total points.Correct! Team A averaged 14 points per match, while Team B averaged 12.5.
Compare the unit rates rather than the total points.
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Hint
Divide the number of wins by the number of matches and multiply by 100.
A team won 9 of its 12 matches. What was its win percentage, rounded to the nearest whole percent?
Correct! The team's win percentage was 75%.
Use wins divided by total matches, then convert the result to a percentage.
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Hint
Find each team's average points per match before comparing performance.
An organizer says Team X must be stronger because it scored 120 total points, while Team Y scored only 105. Team X played 10 matches, and Team Y played 7 matches. Which response best checks the organizer's claim?
The claim is incorrect because Team Y averaged 15 points per match, while Team X averaged 12.The claim is correct because 120 is greater than 105.The claim is incorrect because teams with fewer matches are always stronger.The teams cannot be compared using points per match.Correct! Team Y had the higher scoring rate despite the lower total.
A fair comparison must account for the different numbers of matches played.
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