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

Alright, lets get started.

Suppose the initial number of girls = x

Suppose the initial number of boys = y

The ratio of the number of girls to the number of boys is 3:1 (given in question)

x/y = 3/1

Cross multiply

x = 3 y ...............................equation (1)

one girl drops the class and three more boys sign up means new number of gilrs = x - 1

New number of boys = y + 3

the ratio of the number of girls to the number of boys becomes 5:2

(x-1) / (y+3) = 5/2

Cross multiplying

2 (x-1) = 5 (y+3)

2 x - 2 = 5 y + 15

Adding 2 in both sides

2 x - 2 + 2 = 5 y + 15 + 2

2 x = 5 y + 17 ..........................equation (2)

Putting value of x from equation 1 in equation 2

2 (3 y) = 5 y + 17

6 y = 5 y + 17

Subtracting 5 y in both sides

6 y - 5 y = 5 y + 17 - 5 y

y = 17

Putting the value of y in equation 1

x = 3 * 17 = 51

x = 51

After the changes, 1 girl drops : 51 - 1 = 50 new numbers of girls

After the changes, 3 more boys sign up : 17 + 3 = 20 new number of boys

So, total students in the class after changes : 50 + 20 = 70 students : Answer

Hope it will help :)