The number of boys to the number of girls in Primary 6 Patience was 3 : 5. The number of boys to the number of girls in Primary 6 Goodness was 4 : 5. Both classes had the same number of boys. When 18 girls from Primary 6 Patience joined Primary 6 Goodness, the ratio of the number of boys to the number of girls in Primary 6 Patience became 6 : 7. Find the total enrolment of both classes.

Primary 6 Patience		Primary 6 Goodness
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 6 Patience		Primary 6 Goodness
	Boys	Girls	Boys	Girls
Before	12 u	20 u	12 u	15 u
Change		- 18		+ 18
After	6x2 = 12 u	7x2 = 14 u	12 u	15 u + 18

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

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

6 u = 18

1 u = 18 ÷ 6 = 3

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

Answer(s): 177