The number of boys to the number of girls in Primary 5 Peace 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 15 girls from Primary 5 Peace joined Primary 5 Patience, the ratio of the number of boys to the number of girls in Primary 5 Peace became 4 : 5. Find the total enrolment of both classes.

Primary 5 Peace		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 Peace		Primary 5 Patience
	Boys	Girls	Boys	Girls
Before	12 u	20 u	12 u	15 u
Change		- 15		+ 15
After	4x3 = 12 u	5x3 = 15 u	12 u	15 u + 15

The number of boys in Primary 5 Peace remains unchanged.  Make the number of boys in Primary 5 the same.  LCM of 12 and 4 is 12.

Number of girls from Primary 5 Peace that joined Primary 5 Patience
= 20 u - 15 u
= 5 u

5 u = 15

1 u = 15 ÷ 5 = 3

Total enrolment of both classes
= 12 u + 20 u + 12 u + 15 u
= 59 u
= 59 x 3
= 177

Answer(s): 177