+231 In Psychology 101, the ratio of the number of girls to the number of boys is 3:2. After seven more girls join the class, and two boys drop the class, 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?
+105 ah. sorry about that! i think i made a careless mistake :(( (even tho, of course i care! :))
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
