The number of boys to the number of girls in Primary 2 Gentleness was 1 : 4. The number of boys to the number of girls in Primary 2 Faithfulness was 4 : 5. Both classes had the same number of boys. When 16 girls from Primary 2 Gentleness joined Primary 2 Faithfulness, the ratio of the number of boys to the number of girls in Primary 2 Gentleness became 1 : 2. Find the total enrolment of both classes.

Primary 2 Gentleness		Primary 2 Faithfulness
Boys	Girls	Boys	Girls
1x4	4x4	4x1	5x1
1x4		1x4
4 u	16 u	4 u	5 u

The number of boys in both classes is the same.  Make the number of boys the same.  LCM of 1 and 4 is 4.

	Primary 2 Gentleness		Primary 2 Faithfulness
	Boys	Girls	Boys	Girls
Before	4 u	16 u	4 u	5 u
Change		- 16		+ 16
After	1x4 = 4 u	2x4 = 8 u	4 u	5 u + 16

The number of boys in Primary 2 Gentleness remains unchanged.  Make the number of boys in Primary 2 the same.  LCM of 4 and 1 is 4.

Number of girls from Primary 2 Gentleness that joined Primary 2 Faithfulness
= 16 u - 8 u
= 8 u

8 u = 16

1 u = 16 ÷ 8 = 2

Total enrolment of both classes
= 4 u + 16 u + 4 u + 5 u
= 29 u
= 29 x 2
= 58

Answer(s): 58