The number of boys to the number of girls in Primary 4 Goodness was 1 : 4. The number of boys to the number of girls in Primary 4 Faithfulness was 2 : 5. Both classes had the same number of boys. When 8 girls from Primary 4 Goodness joined Primary 4 Faithfulness, the ratio of the number of boys to the number of girls in Primary 4 Goodness became 1 : 3. Find the total enrolment of both classes.

Primary 4 Goodness		Primary 4 Faithfulness
Boys	Girls	Boys	Girls
1x2	4x2	2x1	5x1
1x2		1x2
2 u	8 u	2 u	5 u

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

	Primary 4 Goodness		Primary 4 Faithfulness
	Boys	Girls	Boys	Girls
Before	2 u	8 u	2 u	5 u
Change		- 8		+ 8
After	1x2 = 2 u	3x2 = 6 u	2 u	5 u + 8

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

Number of girls from Primary 4 Goodness that joined Primary 4 Faithfulness
= 8 u - 6 u
= 2 u

2 u = 8

1 u = 8 ÷ 2 = 4

Total enrolment of both classes
= 2 u + 8 u + 2 u + 5 u
= 17 u
= 17 x 4
= 68

Answer(s): 68