2022 AMC 8 Problem 21
Attempt Problem 21 of the 2022 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2022 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
21.
Steph scored baskets out of attempts in the first half of a game, and baskets out of attempts in the second half. Candace took attempts in the first half and attempts in the second. In each half, Steph scored a higher percentage of baskets than Candace. Surprisingly they ended with the same overall percentage of baskets scored. How many more baskets did Candace score in the second half than in the first?
Answer: C
Small hint:
Steph made baskets in attempts overall
Big hint:
Candace must also have made baskets total
Solution:
Steph made baskets in attempts. Candace also took attempts, and their overall percentages were the same, so Candace also made baskets.
Let be Candace’s first-half baskets and be her second-half baskets. Then .
Steph’s first-half percentage was , so , giving . Steph’s second-half percentage was , so .
Thus and . Since , the only possibility is and , so .
Thus, the correct answer is C.
Problem 21 in other years
- 1985 AMC 8
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