How many students were originally in the hall?

Question

In a school hall, two-thirds of the students are boys. If 36 girls leave, then there will only be 2/3 of the girls remaining. How many students were originally in the hall?

 

 

Answer 1

Since 2/3 of the girls remain after 36 leave, that means that those 36 girls are 1/3 of the total number of girls. To find the total number of girls: 36* 3 = 108 girls

 

Since 2/3 of the students (originally)in the hall are boys, that means 1/3 are girls. We know that there were originally 108 girls. That means there are twice as many boys: 108 * 2 = 216 boys

 

So the total number of students originally in the hall were: 108 + 216 = 324 students

Answer 2

Let T = number of total students in the hall

B = number of total boys in the hall

G = number of total girls in the hall

 

from the given information:

 

If 2/3 of T = B, therefore the remaining 1/3 T is G. if G - 36 is 2/3 of G, then 

1/3 of G = 36, means G is 108 therefore, T = 324.  

 

Originally, there were 324 students in the hall.