Mrs Seow had a total of 170 white and purple daisies in the ratio of 7 : 3. After she had given away 6 times as many white daisies as purple daisies, the number of white and purple daisies left was in the ratio of 7 : 4. How many more white daisies than purple daisies did she give away?

	White	Purple	Total
Before	7 b	3 b	10 b
Change	- 6 u	- 1 u
After	7 p	4 p

	Make p the same (1)x4 = (3)	White (1)	Purple (2)	Make p the same (2)x7 = (4)
Before	476	119	51	357
Change	- 24 u	- 6 u	- 1 u	- 7 u
After	28 p	7 p	4 p	28 p

Number of daisies at first
= 7 b + 3 b
= 10 b

10 b = 170

1 b = 170 ÷ 10 = 17

Number of white daisies at first
= 7 b
= 7 x 17
= 119

Number of purple daisies at first
= 3 b
= 3 x 17
= 51

119 - 6 u = 7 p --- (1)

51 - 1 u = 4 p --- (2)

Make p the same.

(1)_x4 
476 - 24 u = 28 p --- (3)

(2)_x7 = (4)
357 - 7 u = 28 p --- (4)

(3) = (4)
476 - 24 u = 357 - 7 u
24 u - 7 u = 476 - 357
17 u = 119

1 u = 119 ÷ 17 = 7

Number of more white daisies than purple daisies that she gave away
= 6 u - 1 u
= 5 u
= 5 x 7
= 35

Answer(s): 35