Mrs Lim had a total of 130 purple and white carnations in the ratio of 9 : 4. 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 5 : 3. How many more purple carnations than white carnations did she give away?

	Purple	White	Total
Before	9 b	4 b	13 b
Change	- 4 u	- 1 u
After	5 p	3 p

	Make p the same (1)x3 = (3)	Purple (1)	White (2)	Make p the same (2)x5 = (4)
Before	270	90	40	200
Change	- 12 u	- 4 u	- 1 u	- 5 u
After	15 p	5 p	3 p	15 p

Number of carnations at first
= 9 b + 4 b
= 13 b

13 b = 130

1 b = 130 ÷ 13 = 10

Number of purple carnations at first
= 9 b
= 9 x 10
= 90

Number of white carnations at first
= 4 b
= 4 x 10
= 40

90 - 4 u = 5 p --- (1)

40 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
270 - 12 u = 15 p --- (3)

(2)_x5 = (4)
200 - 5 u = 15 p --- (4)

(3) = (4)
270 - 12 u = 200 - 5 u
12 u - 5 u = 270 - 200
7 u = 70

1 u = 70 ÷ 7 = 10

Number of more purple carnations than white carnations that she gave away
= 4 u - 1 u
= 3 u
= 3 x 10
= 30

Answer(s): 30