Question

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?

Answer 1

There are 68 students in the class after these changes.

Explanation:

g = number of girls

b = number of boys

Because the ratio of girls to boys is 3:1, initally the equation was

g = 3b

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, the new equation is

(g - 1)/(b + 3) = 5/2

Cross multiply.

2(g - 1) = 5(b + 3)

2g - 2 = 5b + 15

2g - 5b = 17

Then, substitute g (which is 3b because the first equation was g = 3b)

2(3b) - 5b = 17

b = 17

g = 3b = 3*17 = 51

g = 51

The final number of students in the class = 17 + 51 = 68

Answer: 68