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 2:3. How many students are in the class after these changes?
let the number of juniors be j and the number of seniors be s.
j/s = 3/2, so j = 3s/2
(j+6)/(s-1) = 2/3
using cross-multiplication, 3j+18 = 2s-2.
substituting j for 3s/2, 9s/2+18 = 2s-2.
s=-38/5 <----- Doesn't make any sense (???)
Guest, are you sure the problem is correct? Intuitively, if there are more juniors and less seniors, the new ratio would have been with more juniors and less seniors. For example, in this similar problem: https://web2.0calc.com/questions/help-pls_10673, the ratio increases.
Did I make a mistake in my calculations? If so, please point it out. Thank you!