+0  
 
+1
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avatar+1791 

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?

 Jan 9, 2024
 #1
avatar+128732 
+1

J /  S = 3/2

 

J =  (3/2)S

 

( J + 12 )  / ( S  - 1)  =   2/1

 

((3/2)S+ 12) /  (  S  -- 1)    =  2/1               cross-multiply

 

(3/2)S + 12  = 2 (S - 1)

 

(3/2)S + 12  = 2S   - 2

 

12 + 2 =  2S - (3/2)S

 

14 =  (1/2)S

 

14 ( 2/1)  = S

 

28  = S

 

J = (3/2)(28)  =  42

 

After changes    J + 12 =  54           S - 1 =  27

 

54 +  27   =    

 

81 total  students

 

 

cool cool cool

 Jan 9, 2024
edited by CPhill  Jan 9, 2024

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