Make the Track Team

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Several eighth graders tried out for the track team.

 After Round 1,  1/2 of the students were eliminated.
 After Round 2,  1/3 of the students were eliminated.
 After Round 3,  1/4 of the students were eliminated.
 After Round 4,  1/5 of the students were eliminated.

The 12 students who remained made the team.  How many eighth graders originally tried out?

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Answer:  60

 

Strategy: Work Backward

1/5 of 15 = 3, so before Round 4, there were 12+3, or 15

1/4 of 20 = 5, so before Round 3, there were 15+5, or 20

1/3 of 30 = 10, so before Round 2, there were 20+10, or 30

1/2 of 60 = 30, so before Round 1, there were 30+30, or 60

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