2009 AMC 8 Problem 23
Attempt Problem 23 of the 2009 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 2009 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
23.
On the last day of school, Mrs. Wonderful gave jelly beans to her class. She gave each boy as many jelly beans as there were boys in the class. She gave each girl as many jelly beans as there were girls in the class. She brought jelly beans, and when she finished, she had six jelly beans left. There were two more boys than girls in her class. How many students were in her class?
Small hint:
Let the number of girls be so the number of boys is
Big hint:
The total jelly beans given out is
Solution:
Let be the number of boys in the class and be the number of girls. From the problem, we get that
If each boy gets jelly beans, then Mrs. Wonderful will give out a total of jelly beans to all the boys. Similarly, she will give out jelly beans to all the girls.
Therefore, Since cannot be negative, we get that This means that so
Thus, B is the correct answer.
Problem 23 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
- 2001 AMC 8
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- 2004 AMC 8
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- 2006 AMC 8
- 2007 AMC 8
- 2008 AMC 8
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