Brent, I don't understand that approach. Why start with two variables B and G? Is that the only way to tackle this problem?

PS: nice question : P

Another approach

let total number of students be T
let total number of students in future = T-40

number of boys = 3T/8
number of boys in future = 2(T-40)/7

Number of Boys decreased by 20
Hence
3T/8 - 20 = 2(T-40)/7
21T - (20*8*7) = 16T - (80*8)
5T = (20*8*7) - (80*8)
5T = (80*14) - (80*8)
T = (80*6)/5 = 16*6 = 96

hutch27 wrote:at ABC academy, the ratio of the number of girls to the number of boys is 5 to 3. if 20 boys and 20 girls were to leave, the ratio of the number of boys to the number of girls would be 2 to 5. How many children are at ABC academy?

A 56
B 60
C 72
D 84
E 96

An alternate -- and perhaps the fastest -- approach is to plug in the answer choices, which represent the total number of children.

G:B = 5:3, implying that there are 5 girls for every 3 boys.
Since = 5+3 = 8, the total number of children must be a multiple of 8.
Eliminate B and D.

After 40 children leave, G:B = 5:2, implying that there are 5 girls for every 2 boys.
Since 5+2 = 7, the resulting number of children must be a multiple of 7.
Thus, when 40 is subtracted from the correct answer choice, the result must be a multiple of 7:
A: 56-40 = 16.
C: 72-40 = 32.
E: 96-40 = 56.

Only the result in red is a multiple of 7.

The correct answer is E.