Question

The ratio of the number of girls to the number of boys in a stamp club was 3 : 2 last year. When 15 boys joined the club this year, the ratio became 2 : 3. Find the total number of children in the club this year.

Answer 1

let the number of girls be 3x and the number of boys 2x
(notice 3x : 2x = 3 : 2 )

after the addition of boys
number of girls = 3x
number of boys = 2x + 15

3x : 2x+15 = 2:3
3x/(2x+15) = 2/3
9x = 4x + 30
5x = 30
x = 6
current number of girls = 18
current number of boys = 27

so number of children in the club now
= 3x + 2x+15 = 5x + 15
= 5(6) + 15 = 45

check:
original: girls = 18, boys = 12, notice ratio is 18:12 = 3:2
after: girls = 18 , boys = 27 , notice 18:27 = 2:3
and 18+27 = 45

all is well.