Mrs Lin had a total of 120 pink and purple lilies in the ratio of 5 : 3. After she had given away 5 times as many pink lilies as purple lilies, the number of pink and purple lilies left was in the ratio of 5 : 4. How many more pink lilies than purple lilies did she give away?

	Pink	Purple	Total
Before	5 b	3 b	8 b
Change	- 5 u	- 1 u
After	5 p	4 p

	Make p the same (1)x4 = (3)	Pink (1)	Purple (2)	Make p the same (2)x5 = (4)
Before	300	75	45	225
Change	- 20 u	- 5 u	- 1 u	- 5 u
After	20 p	5 p	4 p	20 p

Number of lilies at first
= 5 b + 3 b
= 8 b

8 b = 120

1 b = 120 ÷ 8 = 15

Number of pink lilies at first
= 5 b
= 5 x 15
= 75

Number of purple lilies at first
= 3 b
= 3 x 15
= 45

75 - 5 u = 5 p --- (1)

45 - 1 u = 4 p --- (2)

Make p the same.

(1)_x4 
300 - 20 u = 20 p --- (3)

(2)_x5 = (4)
225 - 5 u = 20 p --- (4)

(3) = (4)
300 - 20 u = 225 - 5 u
20 u - 5 u = 300 - 225
15 u = 75

1 u = 75 ÷ 15 = 5

Number of more pink lilies than purple lilies that she gave away
= 5 u - 1 u
= 4 u
= 4 x 5
= 20

Answer(s): 20