Mrs Seow had a total of 168 white and purple daisies in the ratio of 7 : 5. After she had given away 4 times as many white daisies as purple daisies, the number of white and purple daisies left was in the ratio of 6 : 5. How many more white daisies than purple daisies did she give away?

	White	Purple	Total
Before	7 b	5 b	12 b
Change	- 4 u	- 1 u
After	6 p	5 p

	Make p the same (1)x5 = (3)	White (1)	Purple (2)	Make p the same (2)x6 = (4)
Before	490	98	70	420
Change	- 20 u	- 4 u	- 1 u	- 6 u
After	30 p	6 p	5 p	30 p

Number of daisies at first
= 7 b + 5 b
= 12 b

12 b = 168

1 b = 168 ÷ 12 = 14

Number of white daisies at first
= 7 b
= 7 x 14
= 98

Number of purple daisies at first
= 5 b
= 5 x 14
= 70

98 - 4 u = 6 p --- (1)

70 - 1 u = 5 p --- (2)

Make p the same.

(1)_x5 
490 - 20 u = 30 p --- (3)

(2)_x6 = (4)
420 - 6 u = 30 p --- (4)

(3) = (4)
490 - 20 u = 420 - 6 u
20 u - 6 u = 490 - 420
14 u = 70

1 u = 70 ÷ 14 = 5

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

Answer(s): 15