Mrs Fong had a total of 140 purple and white lilies in the ratio of 7 : 3. After she had given away 5 times as many purple lilies as white lilies, the number of purple and white lilies left was in the ratio of 3 : 2. How many more purple lilies than white lilies did she give away?

	Purple	White	Total
Before	7 b	3 b	10 b
Change	- 5 u	- 1 u
After	3 p	2 p

	Make p the same (1)x2 = (3)	Purple (1)	White (2)	Make p the same (2)x3 = (4)
Before	196	98	42	126
Change	- 10 u	- 5 u	- 1 u	- 3 u
After	6 p	3 p	2 p	6 p

Number of lilies at first
= 7 b + 3 b
= 10 b

10 b = 140

1 b = 140 ÷ 10 = 14

Number of purple lilies at first
= 7 b
= 7 x 14
= 98

Number of white lilies at first
= 3 b
= 3 x 14
= 42

98 - 5 u = 3 p --- (1)

42 - 1 u = 2 p --- (2)

Make p the same.

(1)_x2 
196 - 10 u = 6 p --- (3)

(2)_x3 = (4)
126 - 3 u = 6 p --- (4)

(3) = (4)
196 - 10 u = 126 - 3 u
10 u - 3 u = 196 - 126
7 u = 70

1 u = 70 ÷ 7 = 10

Number of more purple lilies than white lilies that she gave away
= 5 u - 1 u
= 4 u
= 4 x 10
= 40

Answer(s): 40