+1533 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?
+129850 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
