Mrs Chua had a total of 81 white and purple carnations in the ratio of 7 : 2. After she had given away 4 times as many white carnations as purple carnations, the number of white and purple carnations left was in the ratio of 7 : 4. How many more white carnations than purple carnations did she give away?

	White	Purple	Total
Before	7 b	2 b	9 b
Change	- 4 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	252	63	18	126
Change	- 16 u	- 4 u	- 1 u	- 7 u
After	28 p	7 p	4 p	28 p

Number of carnations at first
= 7 b + 2 b
= 9 b

9 b = 81

1 b = 81 ÷ 9 = 9

Number of white carnations at first
= 7 b
= 7 x 9
= 63

Number of purple carnations at first
= 2 b
= 2 x 9
= 18

63 - 4 u = 7 p --- (1)

18 - 1 u = 4 p --- (2)

Make p the same.

(1)_x4 
252 - 16 u = 28 p --- (3)

(2)_x7 = (4)
126 - 7 u = 28 p --- (4)

(3) = (4)
252 - 16 u = 126 - 7 u
16 u - 7 u = 252 - 126
9 u = 126

1 u = 126 ÷ 9 = 14

Number of more white carnations than purple carnations that she gave away
= 4 u - 1 u
= 3 u
= 3 x 14
= 42

Answer(s): 42