The number of boys to the number of girls in Primary 3 Patience was 1 : 4. The number of boys to the number of girls in Primary 3 Faithfulness was 4 : 5. Both classes had the same number of boys. When 16 girls from Primary 3 Patience joined Primary 3 Faithfulness, the ratio of the number of boys to the number of girls in Primary 3 Patience became 1 : 3. Find the total enrolment of both classes.

Primary 3 Patience		Primary 3 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 3 Patience		Primary 3 Faithfulness
	Boys	Girls	Boys	Girls
Before	4 u	16 u	4 u	5 u
Change		- 16		+ 16
After	1x4 = 4 u	3x4 = 12 u	4 u	5 u + 16

The number of boys in Primary 3 Patience remains unchanged.  Make the number of boys in Primary 3 the same.  LCM of 4 and 1 is 4.

Number of girls from Primary 3 Patience that joined Primary 3 Faithfulness
= 16 u - 12 u
= 4 u

4 u = 16

1 u = 16 ÷ 4 = 4

Total enrolment of both classes
= 4 u + 16 u + 4 u + 5 u
= 29 u
= 29 x 4
= 116

Answer(s): 116