Mrs Lau had a total of 220 purple and yellow lilies in the ratio of 7 : 4. After she had given away 4 times as many purple lilies as yellow lilies, the number of purple and yellow lilies left was in the ratio of 3 : 2. How many more purple lilies than yellow lilies did she give away?

	Purple	Yellow	Total
Before	7 b	4 b	11 b
Change	- 4 u	- 1 u
After	3 p	2 p

	Make p the same (1)x2 = (3)	Purple (1)	Yellow (2)	Make p the same (2)x3 = (4)
Before	280	140	80	240
Change	- 8 u	- 4 u	- 1 u	- 3 u
After	6 p	3 p	2 p	6 p

Number of lilies at first
= 7 b + 4 b
= 11 b

11 b = 220

1 b = 220 ÷ 11 = 20

Number of purple lilies at first
= 7 b
= 7 x 20
= 140

Number of yellow lilies at first
= 4 b
= 4 x 20
= 80

140 - 4 u = 3 p --- (1)

80 - 1 u = 2 p --- (2)

Make p the same.

(1)_x2 
280 - 8 u = 6 p --- (3)

(2)_x3 = (4)
240 - 3 u = 6 p --- (4)

(3) = (4)
280 - 8 u = 240 - 3 u
8 u - 3 u = 280 - 240
5 u = 40

1 u = 40 ÷ 5 = 8

Number of more purple lilies than yellow lilies that she gave away
= 4 u - 1 u
= 3 u
= 3 x 8
= 24

Answer(s): 24