Question

A classroom has some students in it. The ratio of boys to girls is 3:2. After a minute, a boy enters the classroom and two girls leave. The ratio of boys to girls is now 2:1. How many students are in the classroom at this point?

Answer 1

24

Explanation:

I'm not sure what formulas apply here, so I just used multiples and elimination to find the answer.

If the starting ratio is b:g--> 3:2 and 1 boy enters and 2 girs leave, the ratio, without figuring the multiples of 3 and 2, would leave you with 4:0 and we know that's not the case, because in the end we still have half the number of girls as we do boys (so we can't have 0 girls). I took multiples of 3 and 2. First I multiplied both by 2 to get a ratio equivalent to 3:2 which is 6:4. Now if 1 boy enters and 2 girls leave, the ratio is 7:2 which does not reduce to 2:1.

Next, I multiplied both by 3 to get a ratio equivalent to 3:2 which is 9:6. Now if 1 boy enters and 2 girls leave, the ratio is 10:4 which does not reduce to 2:1.

Next, I multiplied both by 4 to get a ratio of 12:8. If 1 boy enters and 2 girls leave, the ratio is 13:6 which does not reduce to 2:1.

Next, I multipled both by 5 to get a ratio of 15:10. If 1 boy enters and 2 girls leave, the ratio is 16:8 which does reduce to 2:1.

That means that originally, there were 25 students in the room and at the end of the comings and goings, there were 24.