The number of boys to the number of girls in Primary 2 Joy was 1 : 4. The number of boys to the number of girls in Primary 2 Gentleness was 3 : 5. Both classes had the same number of boys. When 6 girls from Primary 2 Joy joined Primary 2 Gentleness, the ratio of the number of boys to the number of girls in Primary 2 Joy became 1 : 3. Find the total enrolment of both classes.

Primary 2 Joy		Primary 2 Gentleness
Boys	Girls	Boys	Girls
1x3	4x3	3x1	5x1
1x3		1x3
3 u	12 u	3 u	5 u

The number of boys in both classes is the same.  Make the number of boys the same.  LCM of 1 and 3 is 3.

	Primary 2 Joy		Primary 2 Gentleness
	Boys	Girls	Boys	Girls
Before	3 u	12 u	3 u	5 u
Change		- 6		+ 6
After	1x3 = 3 u	3x3 = 9 u	3 u	5 u + 6

The number of boys in Primary 2 Joy remains unchanged.  Make the number of boys in Primary 2 the same.  LCM of 3 and 1 is 3.

Number of girls from Primary 2 Joy that joined Primary 2 Gentleness
= 12 u - 9 u
= 3 u

3 u = 6

1 u = 6 ÷ 3 = 2

Total enrolment of both classes
= 3 u + 12 u + 3 u + 5 u
= 23 u
= 23 x 2
= 46

Answer(s): 46