The number of boys to the number of girls in Primary 5 Gentleness was 3 : 5. The number of boys to the number of girls in Primary 5 Patience was 4 : 5. Both classes had the same number of boys. When 12 girls from Primary 5 Gentleness joined Primary 5 Patience, the ratio of the number of boys to the number of girls in Primary 5 Gentleness became 6 : 7. Find the total enrolment of both classes.

Primary 5 Gentleness		Primary 5 Patience
Boys	Girls	Boys	Girls
3x4	5x4	4x3	5x3
1x12		1x12
12 u	20 u	12 u	15 u

The number of boys in both classes is the same.  Make the number of boys the same.  LCM of 3 and 4 is 12.

	Primary 5 Gentleness		Primary 5 Patience
	Boys	Girls	Boys	Girls
Before	12 u	20 u	12 u	15 u
Change		- 12		+ 12
After	6x2 = 12 u	7x2 = 14 u	12 u	15 u + 12

The number of boys in Primary 5 Gentleness remains unchanged.  Make the number of boys in Primary 5 the same.  LCM of 12 and 6 is 12.

Number of girls from Primary 5 Gentleness that joined Primary 5 Patience
= 20 u - 14 u
= 6 u

6 u = 12

1 u = 12 ÷ 6 = 2

Total enrolment of both classes
= 12 u + 20 u + 12 u + 15 u
= 59 u
= 59 x 2
= 118

Answer(s): 118