The number of boys to the number of girls in Primary 6 Gentleness was 2 : 5. The number of boys to the number of girls in Primary 6 Joy was 3 : 5. Both classes had the same number of boys. When 30 girls from Primary 6 Gentleness joined Primary 6 Joy, the ratio of the number of boys to the number of girls in Primary 6 Gentleness became 2 : 3. Find the total enrolment of both classes.

Primary 6 Gentleness		Primary 6 Joy
Boys	Girls	Boys	Girls
2x3	5x3	3x2	5x2
1x6		1x6
6 u	15 u	6 u	10 u

The number of boys in both classes is the same.  Make the number of boys the same.  LCM of 2 and 3 is 6.

	Primary 6 Gentleness		Primary 6 Joy
	Boys	Girls	Boys	Girls
Before	6 u	15 u	6 u	10 u
Change		- 30		+ 30
After	2x3 = 6 u	3x3 = 9 u	6 u	10 u + 30

The number of boys in Primary 6 Gentleness remains unchanged.  Make the number of boys in Primary 6 the same.  LCM of 6 and 2 is 6.

Number of girls from Primary 6 Gentleness that joined Primary 6 Joy
= 15 u - 9 u
= 6 u

6 u = 30

1 u = 30 ÷ 6 = 5

Total enrolment of both classes
= 6 u + 15 u + 6 u + 10 u
= 37 u
= 37 x 5
= 185

Answer(s): 185