In psychology 101, the ratio of the number of girls to the number of boys is $3: 1$. after one girl drops the class and three more boys sign up, the ratio of the number of girls to the number of boys becomes $5: 2$. how many students are in the class after these changes?

Initially,
g = number of girls;
b = number of boys.
Because the ratio of girls to boys is 3:1, therefore
g = 3b                 (1)

Finally, we have
g-1 girls because one girl dropped the class;
b+3 boys because three more boys signed up.
Because the new ratio of girls to boys is 5:2, therefore
(g - 1)/(b + 3) = 5/2
Cross multiply.
2(g - 1) = 5(b + 3)
2g - 2 = 5b + 15
2g - 5b = 17            (2)

Substitute (1) into (2) to obtain
2(3b) - 5b = 17
b = 17
g = 3b = 3*17 = 51

Final number of students in the class = 17 + 51 = 68

68