several freshmen tried out for the school track team.
after round 1, 1/2 of the freshmen were eliminated. After round 2, 1/3 of those remaining were eliminated. After round 3, 1/4 of those remaining were eliminated. After round 4, 1/5 of those remaining were eliminated. After round 5, 1/6 of those remaining were eliminated. The 10 freshmen who remained made it onto the track team. How many freshmen originally tried out?
the answer is 60. How do I set this up to get my answer.
x = the number you start with
after round 1: you have x/2
1/3 of those are eliminated which means 2/3 remain
Multiply x/2 times 2/3 = x/3
Next round 1/4 are eliminated which means that 3/4 remain.
3/4 times x/3 = x/4
Can you finish from here with rounds 5 and 6
it should end with x/6 = 10 so x would = 60
Set that final answer = 10
To approach this problem, we can work backwards by using the given information and some reverse calculations.
Let's assume that the number of freshmen originally trying out is "x".
After the 1st round, 1/2 of the freshmen were eliminated, so the number of freshmen remaining is (1/2)x.
After the 2nd round, 1/3 of the remaining freshmen were eliminated, so the number of freshmen remaining is (2/3)(1/2)x = (1/3)x.
By continuing this process, we can set up the following progression:
After the 3rd round: (2/4)(1/3)x = (2/9)x
After the 4th round: (3/5)(2/9)x = (6/45)x = (2/15)x
After the 5th round: (4/6)(2/15)x = (8/90)x = (4/45)x
It is given that the 10 freshmen who remained made it onto the track team, so (4/45)x = 10.
To solve for x, we can multiply both sides of the equation by (45/4):
(4/45)x * (45/4) = 10 * (45/4)
x = 450/4
x = 112.5
However, since we're dealing with whole numbers (the number of freshmen), we need to adjust our solution.
We can determine that the closest whole number greater than 112.5 is 113. Therefore, the original number of freshmen who tried out is 113.
So, the answer is 113.