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In Linguistics $101,$ the ratio of the number of juniors to the number of seniors is $3:2$.  When twelve more juniors join the class, and one senior drops the class, the ratio of the number of juniors to the number of seniors becomes $2:1$.  How many students are in the class after these changes?

 Apr 30, 2024

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J / S =  3 / 2

J = (3/2)S

 

[J + 12 ] / [ S - 1 ]  =  2 / 1

 

[ (3/2)S + 12 ]  / [ S - 1 ] = 2 / 1

 

(3/2)S + 12  = 2  [S -1]

 

(3/2)S + 12 = 2S  - 2

 

2S - (3/2)S = 12 + 2

 

(1/2)S  = 14

 

S = 28

J = (3/2)S = (3/2) (28)  = 42

 

After the changes  there are  54 J   and  27 S  =    81  students total

 

cool cool cool

 Apr 30, 2024

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