Mrs Yeo had a total of 112 purple and white daisies in the ratio of 9 : 5. After she had given away 6 times as many purple daisies as white daisies, the number of purple and white daisies left was in the ratio of 6 : 5. How many more purple daisies than white daisies did she give away?

	Purple	White	Total
Before	9 b	5 b	14 b
Change	- 6 u	- 1 u
After	6 p	5 p

	Make p the same (1)x5 = (3)	Purple (1)	White (2)	Make p the same (2)x6 = (4)
Before	360	72	40	240
Change	- 30 u	- 6 u	- 1 u	- 6 u
After	30 p	6 p	5 p	30 p

Number of daisies at first
= 9 b + 5 b
= 14 b

14 b = 112

1 b = 112 ÷ 14 = 8

Number of purple daisies at first
= 9 b
= 9 x 8
= 72

Number of white daisies at first
= 5 b
= 5 x 8
= 40

72 - 6 u = 6 p --- (1)

40 - 1 u = 5 p --- (2)

Make p the same.

(1)_x5 
360 - 30 u = 30 p --- (3)

(2)_x6 = (4)
240 - 6 u = 30 p --- (4)

(3) = (4)
360 - 30 u = 240 - 6 u
30 u - 6 u = 360 - 240
24 u = 120

1 u = 120 ÷ 24 = 5

Number of more purple daisies than white daisies that she gave away
= 6 u - 1 u
= 5 u
= 5 x 5
= 25

Answer(s): 25