AMC 10 Weekly Practice Round 2
Complete problem set with solutions and individual problem pages
In a math competition, the top students received awards. Originally, there were first prize winners, second prize winners, and third prize winners. After an adjustment, the numbers changed to first prize winners, second prize winners, and third prize winners.
After the adjustment:
The average score of first prize winners decreased by points,
The average score of second prize winners decreased by points,
The average score of third prize winners decreased by point.
If the original average score of second prize winners was points higher than that of third prize winners, how many points higher is the adjusted average score of first prize winners compared to that of second prize winners?
- A.
- B.
- C.
- D.
- E.
Let the adjusted average scores of the first, second, and third prize winners be , , and , respectively.
According to the problem:
Simplifying:
Therefore:
Answer: After the adjustment, the average score of the first prize winners is points higher than that of the second prize winners.
