The number of girls to the number of boys in Primary 1 Patience was 1 : 4. The number of girls to the number of boys in Primary 1 Gentleness was 2 : 5. Both classes had the same number of girls. When 12 boys from Primary 1 Patience joined Primary 1 Gentleness, the ratio of the number of girls to the number of boys in Primary 1 Patience became 1 : 2. Find the total enrolment of both classes.

Primary 1 Patience		Primary 1 Gentleness
Girls	Boys	Girls	Boys
1x2	4x2	2x1	5x1
1x2		1x2
2 u	8 u	2 u	5 u

The number of girls in both classes is the same.  Make the number of girls the same.  LCM of 1 and 2 is 2.

	Primary 1 Patience		Primary 1 Gentleness
	Girls	Boys	Girls	Boys
Before	2 u	8 u	2 u	5 u
Change		- 12		+ 12
After	1x2 = 2 u	2x2 = 4 u	2 u	5 u + 12

The number of girls in Primary 1 Patience remains unchanged.  Make the number of girls in Primary 1 the same.  LCM of 2 and 1 is 2.

Number of boys from Primary 1 Patience that joined Primary 1 Gentleness
= 8 u - 4 u
= 4 u

4 u = 12

1 u = 12 ÷ 4 = 3

Total enrolment of both classes
= 2 u + 8 u + 2 u + 5 u
= 17 u
= 17 x 3
= 51

Answer(s): 51