Mrs Chau had a total of 91 yellow and purple lilies in the ratio of 10 : 3. After she had given away 6 times as many yellow lilies as purple lilies, the number of yellow and purple lilies left was in the ratio of 4 : 3. How many more yellow lilies than purple lilies did she give away?

	Yellow	Purple	Total
Before	10 b	3 b	13 b
Change	- 6 u	- 1 u
After	4 p	3 p

	Make p the same (1)x3 = (3)	Yellow (1)	Purple (2)	Make p the same (2)x4 = (4)
Before	210	70	21	84
Change	- 18 u	- 6 u	- 1 u	- 4 u
After	12 p	4 p	3 p	12 p

Number of lilies at first
= 10 b + 3 b
= 13 b

13 b = 91

1 b = 91 ÷ 13 = 7

Number of yellow lilies at first
= 10 b
= 10 x 7
= 70

Number of purple lilies at first
= 3 b
= 3 x 7
= 21

70 - 6 u = 4 p --- (1)

21 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
210 - 18 u = 12 p --- (3)

(2)_x4 = (4)
84 - 4 u = 12 p --- (4)

(3) = (4)
210 - 18 u = 84 - 4 u
18 u - 4 u = 210 - 84
14 u = 126

1 u = 126 ÷ 14 = 9

Number of more yellow lilies than purple lilies that she gave away
= 6 u - 1 u
= 5 u
= 5 x 9
= 45

Answer(s): 45