Mrs Yeo had a total of 42 purple and pink lilies in the ratio of 5 : 2. After she had given away 3 times as many purple lilies as pink lilies, the number of purple and pink lilies left was in the ratio of 3 : 2. How many more purple lilies than pink lilies did she give away?

	Purple	Pink	Total
Before	5 b	2 b	7 b
Change	- 3 u	- 1 u
After	3 p	2 p

	Make p the same (1)x2 = (3)	Purple (1)	Pink (2)	Make p the same (2)x3 = (4)
Before	60	30	12	36
Change	- 6 u	- 3 u	- 1 u	- 3 u
After	6 p	3 p	2 p	6 p

Number of lilies at first
= 5 b + 2 b
= 7 b

7 b = 42

1 b = 42 ÷ 7 = 6

Number of purple lilies at first
= 5 b
= 5 x 6
= 30

Number of pink lilies at first
= 2 b
= 2 x 6
= 12

30 - 3 u = 3 p --- (1)

12 - 1 u = 2 p --- (2)

Make p the same.

(1)_x2 
60 - 6 u = 6 p --- (3)

(2)_x3 = (4)
36 - 3 u = 6 p --- (4)

(3) = (4)
60 - 6 u = 36 - 3 u
6 u - 3 u = 60 - 36
3 u = 24

1 u = 24 ÷ 3 = 8

Number of more purple lilies than pink lilies that she gave away
= 3 u - 1 u
= 2 u
= 2 x 8
= 16

Answer(s): 16