SOLUTION: 28 students from the fourth grade competed in a math competition. Each student earned a different number of points. The number of students who received more points than Tom's i

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Question 1070037: 28 students from the fourth grade competed in a math competition.
Each student earned a different number of points. The number of
students who received more points than Tom's is two times smaller
than the number of students who had fewer points than Tom.
In which position did Tom finish that competition?
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
you need to separate the population of 27 students (27 = 28-1, this 1 is Tom) in two disjoint groups in a way that population
of the larger group is two times the population of the smaller group.


These groups are 9 and 18 students:

x + 2x = 27

gives 3x = 27 and x = 9,

so Tom is in 10-th position.


Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
28 students from the fourth grade competed in a math competition.
Each student earned a different number of points. The number of
students who received more points than Tom's is two times smaller
than the number of students who had fewer points than Tom.
In which position did Tom finish that competition?
There are 27 students besides Tom.

Let x = the number of students who received more points than Tom's

Then to find the number of students who had fewer points than Tom,
we must subtract x from 27, and get 27-x

So 27-x = the number of students who had fewer points than Tom.

The number of students who received more points than Tom's is two 
times smaller than the number of students who had fewer points than Tom.

That can be rewritten as

The number of students who had fewer points than Tom is two 
times LARGER than the number of students who received more points 
than Tom.

So 27-x = 2x

     27 = 3x
      
      9 = x 

Since x = the number of students who received more points than Tom,
then 9 received more points , so Tom was in 10th place.

Edwin
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