Mrs Ee had a total of 91 white and purple lilies in the ratio of 9 : 4. After she had given away 4 times as many white lilies as purple lilies, the number of white and purple lilies left was in the ratio of 5 : 3. How many more white lilies than purple lilies did she give away?

	White	Purple	Total
Before	9 b	4 b	13 b
Change	- 4 u	- 1 u
After	5 p	3 p

	Make p the same (1)x3 = (3)	White (1)	Purple (2)	Make p the same (2)x5 = (4)
Before	189	63	28	140
Change	- 12 u	- 4 u	- 1 u	- 5 u
After	15 p	5 p	3 p	15 p

Number of lilies at first
= 9 b + 4 b
= 13 b

13 b = 91

1 b = 91 ÷ 13 = 7

Number of white lilies at first
= 9 b
= 9 x 7
= 63

Number of purple lilies at first
= 4 b
= 4 x 7
= 28

63 - 4 u = 5 p --- (1)

28 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
189 - 12 u = 15 p --- (3)

(2)_x5 = (4)
140 - 5 u = 15 p --- (4)

(3) = (4)
189 - 12 u = 140 - 5 u
12 u - 5 u = 189 - 140
7 u = 49

1 u = 49 ÷ 7 = 7

Number of more white lilies than purple lilies that she gave away
= 4 u - 1 u
= 3 u
= 3 x 7
= 21

Answer(s): 21