The number of girls to the number of boys in Primary 3 Gentleness was 2 : 5. The number of girls to the number of boys in Primary 3 Goodness was 3 : 4. Both classes had the same number of girls. When 10 boys from Primary 3 Gentleness joined Primary 3 Goodness, the ratio of the number of girls to the number of boys in Primary 3 Gentleness became 3 : 5. Find the total enrolment of both classes.

Primary 3 Gentleness		Primary 3 Goodness
Girls	Boys	Girls	Boys
2x3	5x3	3x2	4x2
1x6		1x6
6 u	15 u	6 u	8 u

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

	Primary 3 Gentleness		Primary 3 Goodness
	Girls	Boys	Girls	Boys
Before	6 u	15 u	6 u	8 u
Change		- 10		+ 10
After	3x2 = 6 u	5x2 = 10 u	6 u	8 u + 10

The number of girls in Primary 3 Gentleness remains unchanged.  Make the number of girls in Primary 3 the same.  LCM of 6 and 3 is 6.

Number of boys from Primary 3 Gentleness that joined Primary 3 Goodness
= 15 u - 10 u
= 5 u

5 u = 10

1 u = 10 ÷ 5 = 2

Total enrolment of both classes
= 6 u + 15 u + 6 u + 8 u
= 35 u
= 35 x 2
= 70

Answer(s): 70