In Linguistics $101,$ the ratio of the number of juniors to the number of seniors is $3:2$. When twleve 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?

Question

In Linguistics $101,$ the ratio of the number of juniors to the number of seniors is $3:2$.  When twleve 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?

Bot GPT 3.5 · Answer

We use algebra to solve this problem. Suppose there are $3x$ juniors and $2x$ seniors in the class, for some positive integer $x$. Then $(3x+12)/(2x-1)=2/1=2$, or $3x+12=4x-2$, or $14=x$. Hence there are $2 \cdot 14 = \boxed{28}$ students in the class.