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avatar+1280 

In Linguistics $101,$ the ratio of the number of juniors to the number of seniors is $3:2$.  When $6$ more juniors join the class, and $1$ senior drops the class, the ratio of the number of juniors to the number of seniors becomes $18:7$.  How many students are in the class after these changes?

 Jan 1, 2024
 #1
avatar+129185 
+1

At first   J / S  =  3 /2  ⇒     J = (3/2)S        (1)

 

After the changes we have

 

[J + 6 ] / [ S - 1 ]  = 18/7     (2)

 

Sub (1) into (2)

 

[(3/2)S + 6 ] / [ S - 1 ] =  18/7

 

(3/2)S + 6 =  (18/7) [S-1]

 

(3/2)S + 6 =   (18/7)S - 18/7

 

6 + 18/7 =   (18/7)S - (3/2)S           multiply though by common denominator of 2,7  = 14

 

84 + 36  =  36S - 21S

 

120 =  15S

 

S =  120 / 15  =  8

 

J = (3/2)(8)  =  12

 

After changes   J + S  =  [ 12 + 6 ]  + [ 8 -1] =  25

 

cool cool cool

 Jan 2, 2024

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