The number of boys to the number of girls in Primary 6 Gentleness was 2 : 5. The number of boys to the number of girls in Primary 6 Patience was 4 : 5. Both classes had the same number of boys. When 4 girls from Primary 6 Gentleness joined Primary 6 Patience, the ratio of the number of boys to the number of girls in Primary 6 Gentleness became 1 : 2. Find the total enrolment of both classes.

Primary 6 Gentleness		Primary 6 Patience
Boys	Girls	Boys	Girls
2x2	5x2	4x1	5x1
1x4		1x4
4 u	10 u	4 u	5 u

The number of boys in both classes is the same.  Make the number of boys the same.  LCM of 2 and 4 is 4.

	Primary 6 Gentleness		Primary 6 Patience
	Boys	Girls	Boys	Girls
Before	4 u	10 u	4 u	5 u
Change		- 4		+ 4
After	1x4 = 4 u	2x4 = 8 u	4 u	5 u + 4

The number of boys in Primary 6 Gentleness remains unchanged.  Make the number of boys in Primary 6 the same.  LCM of 4 and 1 is 4.

Number of girls from Primary 6 Gentleness that joined Primary 6 Patience
= 10 u - 8 u
= 2 u

2 u = 4

1 u = 4 ÷ 2 = 2

Total enrolment of both classes
= 4 u + 10 u + 4 u + 5 u
= 23 u
= 23 x 2
= 46

Answer(s): 46