The number of girls to the number of boys in Primary 3 Faithfulness was 1 : 4. The number of girls to the number of boys in Primary 3 Peace was 3 : 5. Both classes had the same number of girls. When 12 boys from Primary 3 Faithfulness joined Primary 3 Peace, the ratio of the number of girls to the number of boys in Primary 3 Faithfulness became 1 : 2. Find the total enrolment of both classes.

Primary 3 Faithfulness		Primary 3 Peace
Girls	Boys	Girls	Boys
1x3	4x3	3x1	5x1
1x3		1x3
3 u	12 u	3 u	5 u

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

	Primary 3 Faithfulness		Primary 3 Peace
	Girls	Boys	Girls	Boys
Before	3 u	12 u	3 u	5 u
Change		- 12		+ 12
After	1x3 = 3 u	2x3 = 6 u	3 u	5 u + 12

The number of girls in Primary 3 Faithfulness remains unchanged.  Make the number of girls in Primary 3 the same.  LCM of 3 and 1 is 3.

Number of boys from Primary 3 Faithfulness that joined Primary 3 Peace
= 12 u - 6 u
= 6 u

6 u = 12

1 u = 12 ÷ 6 = 2

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

Answer(s): 46