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Reim and Bindu are in a line with other students, waiting to see a movie. There are at most 30 students in the line. Reim says: “There are three times as many students after me in this line than before me.” Bindu says: “There are four times as many students after me in this line than before me.” How many students are in the line?

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Let there be k students in front of Reim.

So there is  k students in front + 3k students behind + Reim = 4k+1 students

 

Let N be the number of students in front of Bindu. 

So there is N students in front + 4N students behind + Bindu = 5N+1 students

 

4k+1=5N+1

4k=5N

 

So the number of students is a product of both 4 and 5 + 1 more

20 is the only such product that is less than or equal to 30

 

So there are 21 students in the line.

Bindu is 5th and Reim is 6th.

 May 3, 2020

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