Mrs Ng had a total of 168 white and purple carnations in the ratio of 9 : 5. After she had given away 6 times as many white carnations as purple carnations, the number of white and purple carnations left was in the ratio of 4 : 3. How many more white carnations than purple carnations did she give away?

	White	Purple	Total
Before	9 b	5 b	14 b
Change	- 6 u	- 1 u
After	4 p	3 p

	Make p the same (1)x3 = (3)	White (1)	Purple (2)	Make p the same (2)x4 = (4)
Before	324	108	60	240
Change	- 18 u	- 6 u	- 1 u	- 4 u
After	12 p	4 p	3 p	12 p

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

14 b = 168

1 b = 168 ÷ 14 = 12

Number of white carnations at first
= 9 b
= 9 x 12
= 108

Number of purple carnations at first
= 5 b
= 5 x 12
= 60

108 - 6 u = 4 p --- (1)

60 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
324 - 18 u = 12 p --- (3)

(2)_x4 = (4)
240 - 4 u = 12 p --- (4)

(3) = (4)
324 - 18 u = 240 - 4 u
18 u - 4 u = 324 - 240
14 u = 84

1 u = 84 ÷ 14 = 6

Number of more white carnations than purple carnations that she gave away
= 6 u - 1 u
= 5 u
= 5 x 6
= 30

Answer(s): 30