2007 AMC 10B Problems/Problem 14
- The following problem is from both the 2007 AMC 12B #10 and 2007 AMC 10B #14, so both problems redirect to this page.
Problem
Some boys and girls are having a car wash to raise money for a class trip to China. Initially of the group are girls. Shortly thereafter two girls leave and two boys arrive, and then of the group are girls. How many girls were initially in the group?
Solution
If we let be the number of people initially in the group, then is the number of girls. If two girls leave and two boys arrive, the number of people in the group is still , but the number of girls is . Since only of the group are girls, The number of girls initially in the group is
Alternate Solution
There are the same number of total people before and after, but the number of girls has dropped by two or of the total. , and , so the answer is .
Yet Another Alternate Solution
Let be the number of people initially in the group and the number of girls. , so . Also, the problem states . Substituting in terms of into the second equation yields that .
~mobius247
See Also
2007 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 9 |
Followed by Problem 11 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
2007 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.