The number of girls to the number of boys in Primary 5 Gentleness was 3 : 5. The number of girls to the number of boys in Primary 5 Patience was 5 : 6. Both classes had the same number of girls. When 8 boys from Primary 5 Gentleness joined Primary 5 Patience, the ratio of the number of girls to the number of boys in Primary 5 Gentleness became 5 : 7. Find the total enrolment of both classes.

Primary 5 Gentleness		Primary 5 Patience
Girls	Boys	Girls	Boys
3x5	5x5	5x3	6x3
1x15		1x15
15 u	25 u	15 u	18 u

The number of girls in both classes is the same.  Make the number of girls the same.  LCM of 3 and 5 is 15.

	Primary 5 Gentleness		Primary 5 Patience
	Girls	Boys	Girls	Boys
Before	15 u	25 u	15 u	18 u
Change		- 8		+ 8
After	5x3 = 15 u	7x3 = 21 u	15 u	18 u + 8

The number of girls in Primary 5 Gentleness remains unchanged.  Make the number of girls in Primary 5 the same.  LCM of 15 and 5 is 15.

Number of boys from Primary 5 Gentleness that joined Primary 5 Patience
= 25 u - 21 u
= 4 u

4 u = 8

1 u = 8 ÷ 4 = 2

Total enrolment of both classes
= 15 u + 25 u + 15 u + 18 u
= 73 u
= 73 x 2
= 146

Answer(s): 146