Mrs Choo had a total of 126 white and purple carnations in the ratio of 9 : 5. After she had given away 3 times as many white carnations as purple carnations, the number of white and purple carnations left was in the ratio of 3 : 2. How many more white carnations than purple carnations did she give away?

	White	Purple	Total
Before	9 b	5 b	14 b
Change	- 3 u	- 1 u
After	3 p	2 p

	Make p the same (1)x2 = (3)	White (1)	Purple (2)	Make p the same (2)x3 = (4)
Before	162	81	45	135
Change	- 6 u	- 3 u	- 1 u	- 3 u
After	6 p	3 p	2 p	6 p

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

14 b = 126

1 b = 126 ÷ 14 = 9

Number of white carnations at first
= 9 b
= 9 x 9
= 81

Number of purple carnations at first
= 5 b
= 5 x 9
= 45

81 - 3 u = 3 p --- (1)

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

Make p the same.

(1)_x2 
162 - 6 u = 6 p --- (3)

(2)_x3 = (4)
135 - 3 u = 6 p --- (4)

(3) = (4)
162 - 6 u = 135 - 3 u
6 u - 3 u = 162 - 135
3 u = 27

1 u = 27 ÷ 3 = 9

Number of more white carnations than purple carnations that she gave away
= 3 u - 1 u
= 2 u
= 2 x 9
= 18

Answer(s): 18