I need help to set up this proportion

In Linguistics $101,$ the ratio of the number of juniors to the number of seniors is $3:2$. When six more juniors join the class, and one 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?

maximum Aug 4, 2023

#1**-1 **

Call the number of original Juniors = J Call the number of original Seniors = S

And we know that

J / S = 3 / 2 so that J = (3/2)S (1)

When 6 more Juniors join and one Senior leaves, we have

[ J + 6 ] / [ S -1 ] = 18 / 7 (2)

Sub (1) into (2)

[(3/2)S + 6] / [ S-1] = 18 / 7 cross-multiply

7 [(3/2)S + 6] = 18 [ S - 1] simplify

(21/2)S + 42 = 18S - 18

42 + 18 = 18S - (21/2)S

60 = (36/2)S - (21/2)S

60 = (15/2)S multiply through by 2

120 = 15S

S = 120 / 15 = 8 = number of seniors in original class

J = (3/2)S (3/2) (8) = 12 = number of Juniors in original class

After 6 Juniors join and 1 Senior leaves...we have the ratio (12 + 6) / (8 -1) = 18 / 7

So....there are 25 total students in the class after the changes

CPhill Aug 4, 2023