+1859 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?
+129771 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
