Mrs Sher had a total of 280 pink and purple lilies in the ratio of 9 : 5. After she had given away 4 times as many pink lilies as purple lilies, the number of pink and purple lilies left was in the ratio of 3 : 2. How many more pink lilies than purple lilies did she give away?

	Pink	Purple	Total
Before	9 b	5 b	14 b
Change	- 4 u	- 1 u
After	3 p	2 p

	Make p the same (1)x2 = (3)	Pink (1)	Purple (2)	Make p the same (2)x3 = (4)
Before	360	180	100	300
Change	- 8 u	- 4 u	- 1 u	- 3 u
After	6 p	3 p	2 p	6 p

Number of lilies at first
= 9 b + 5 b
= 14 b

14 b = 280

1 b = 280 ÷ 14 = 20

Number of pink lilies at first
= 9 b
= 9 x 20
= 180

Number of purple lilies at first
= 5 b
= 5 x 20
= 100

180 - 4 u = 3 p --- (1)

100 - 1 u = 2 p --- (2)

Make p the same.

(1)_x2 
360 - 8 u = 6 p --- (3)

(2)_x3 = (4)
300 - 3 u = 6 p --- (4)

(3) = (4)
360 - 8 u = 300 - 3 u
8 u - 3 u = 360 - 300
5 u = 60

1 u = 60 ÷ 5 = 12

Number of more pink lilies than purple lilies that she gave away
= 4 u - 1 u
= 3 u
= 3 x 12
= 36

Answer(s): 36