Mrs Yap had a total of 55 purple and white carnations in the ratio of 8 : 3. After she had given away 4 times as many purple carnations as white carnations, the number of purple and white carnations left was in the ratio of 3 : 2. How many more purple carnations than white carnations did she give away?

	Purple	White	Total
Before	8 b	3 b	11 b
Change	- 4 u	- 1 u
After	3 p	2 p

	Make p the same (1)x2 = (3)	Purple (1)	White (2)	Make p the same (2)x3 = (4)
Before	80	40	15	45
Change	- 8 u	- 4 u	- 1 u	- 3 u
After	6 p	3 p	2 p	6 p

Number of carnations at first
= 8 b + 3 b
= 11 b

11 b = 55

1 b = 55 ÷ 11 = 5

Number of purple carnations at first
= 8 b
= 8 x 5
= 40

Number of white carnations at first
= 3 b
= 3 x 5
= 15

40 - 4 u = 3 p --- (1)

15 - 1 u = 2 p --- (2)

Make p the same.

(1)_x2 
80 - 8 u = 6 p --- (3)

(2)_x3 = (4)
45 - 3 u = 6 p --- (4)

(3) = (4)
80 - 8 u = 45 - 3 u
8 u - 3 u = 80 - 45
5 u = 35

1 u = 35 ÷ 5 = 7

Number of more purple carnations than white carnations that she gave away
= 4 u - 1 u
= 3 u
= 3 x 7
= 21

Answer(s): 21