Mrs Ang had a total of 91 purple and yellow lilies in the ratio of 8 : 5. 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 6 : 5. How many more purple lilies than yellow lilies did she give away?

	Purple	Yellow	Total
Before	8 b	5 b	13 b
Change	- 4 u	- 1 u
After	6 p	5 p

	Make p the same (1)x5 = (3)	Purple (1)	Yellow (2)	Make p the same (2)x6 = (4)
Before	280	56	35	210
Change	- 20 u	- 4 u	- 1 u	- 6 u
After	30 p	6 p	5 p	30 p

Number of lilies at first
= 8 b + 5 b
= 13 b

13 b = 91

1 b = 91 ÷ 13 = 7

Number of purple lilies at first
= 8 b
= 8 x 7
= 56

Number of yellow lilies at first
= 5 b
= 5 x 7
= 35

56 - 4 u = 6 p --- (1)

35 - 1 u = 5 p --- (2)

Make p the same.

(1)_x5 
280 - 20 u = 30 p --- (3)

(2)_x6 = (4)
210 - 6 u = 30 p --- (4)

(3) = (4)
280 - 20 u = 210 - 6 u
20 u - 6 u = 280 - 210
14 u = 70

1 u = 70 ÷ 14 = 5

Number of more purple lilies than yellow lilies that she gave away
= 4 u - 1 u
= 3 u
= 3 x 5
= 15

Answer(s): 15