The number of boys to the number of girls in Primary 6 Goodness was 3 : 5. The number of boys to the number of girls in Primary 6 Kindness was 5 : 6. Both classes had the same number of boys. When 10 girls from Primary 6 Goodness joined Primary 6 Kindness, the ratio of the number of boys to the number of girls in Primary 6 Goodness became 3 : 4. Find the total enrolment of both classes.

Primary 6 Goodness		Primary 6 Kindness
Boys	Girls	Boys	Girls
3x5	5x5	5x3	6x3
1x15		1x15
15 u	25 u	15 u	18 u

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

	Primary 6 Goodness		Primary 6 Kindness
	Boys	Girls	Boys	Girls
Before	15 u	25 u	15 u	18 u
Change		- 10		+ 10
After	3x5 = 15 u	4x5 = 20 u	15 u	18 u + 10

The number of boys in Primary 6 Goodness remains unchanged.  Make the number of boys in Primary 6 the same.  LCM of 15 and 3 is 15.

Number of girls from Primary 6 Goodness that joined Primary 6 Kindness
= 25 u - 20 u
= 5 u

5 u = 10

1 u = 10 ÷ 5 = 2

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

Answer(s): 146