SOLUTION: A number of freshman tried out for the track team. after the first round of tryouts, 1/2 of the freshmen were cut. after the second round, 1/3 of the freshmen were cut. after

Question 817273: A number of freshman tried out for the track team.
after the first round of tryouts, 1/2 of the freshmen were cut.
after the second round, 1/3 of the freshmen were cut.
after the third round, 1/4 of the freshmen were cut.
after the fourth round 1/5 of the freshmen were cut.
after the fifth round, 1/6 of the freshmen were cut.
There were 10 freshmen left who made the team. How many tried out initially?
Answer by jsmallt9(3759) (Show Source): You can put this solution on YOUR website!
The key to this problem is to focus on the fraction of freshmen who were not cut, not on the fraction that were cut.

Let x = the initial number of freshmen who tried out.
After the first round 1/2 were cut. If 1/2 were cut then 1/2 were not cut. So

would be the number who were not cut during the first round. In the next round 1/3 were cut. So 2/3 were not cut making:

the number of freshmen not cut after two rounds. Next 1/4 were cut and 3/4 were not. So:

were still in it after 3 rounds. Then 1/5 were cut and 4/5 were not making

the number of freshmen who were not cut after 4 rounds. Next 1/6 were cut and 5/6 were not. So:

After all this there were 10 left. So:

Now we solve for x. A lot of canceling can be done on the left side:

leaving:

which simplifies to:

Multiplying by 6:

Check:
60
Keep 1/2 => 30
Keep 2/3 => 20
Keep 3/4 => 15
Keep 4/5 => 12
Keep 5/6 => 10 Check!
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