Mrs Yong had a total of 88 purple and white carnations in the ratio of 5 : 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 5 : 4. How many more purple carnations than white carnations did she give away?

	Purple	White	Total
Before	5 b	3 b	8 b
Change	- 4 u	- 1 u
After	5 p	4 p

	Make p the same (1)x4 = (3)	Purple (1)	White (2)	Make p the same (2)x5 = (4)
Before	220	55	33	165
Change	- 16 u	- 4 u	- 1 u	- 5 u
After	20 p	5 p	4 p	20 p

Number of carnations at first
= 5 b + 3 b
= 8 b

8 b = 88

1 b = 88 ÷ 8 = 11

Number of purple carnations at first
= 5 b
= 5 x 11
= 55

Number of white carnations at first
= 3 b
= 3 x 11
= 33

55 - 4 u = 5 p --- (1)

33 - 1 u = 4 p --- (2)

Make p the same.

(1)_x4 
220 - 16 u = 20 p --- (3)

(2)_x5 = (4)
165 - 5 u = 20 p --- (4)

(3) = (4)
220 - 16 u = 165 - 5 u
16 u - 5 u = 220 - 165
11 u = 55

1 u = 55 ÷ 11 = 5

Number of more purple carnations than white carnations that she gave away
= 4 u - 1 u
= 3 u
= 3 x 5
= 15

Answer(s): 15