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

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

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

	Primary 5 Goodness		Primary 5 Patience
	Girls	Boys	Girls	Boys
Before	12 u	20 u	12 u	15 u
Change		- 12		+ 12
After	3x4 = 12 u	4x4 = 16 u	12 u	15 u + 12

The number of girls in Primary 5 Goodness remains unchanged.  Make the number of girls in Primary 5 the same.  LCM of 12 and 3 is 12.

Number of boys from Primary 5 Goodness that joined Primary 5 Patience
= 20 u - 16 u
= 4 u

4 u = 12

1 u = 12 ÷ 4 = 3

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

Answer(s): 177