Mrs Seow had a total of 143 purple and pink carnations in the ratio of 8 : 5. After she had given away 4 times as many purple carnations as pink carnations, the number of purple and pink carnations left was in the ratio of 5 : 4. How many more purple carnations than pink carnations did she give away?

	Purple	Pink	Total
Before	8 b	5 b	13 b
Change	- 4 u	- 1 u
After	5 p	4 p

	Make p the same (1)x4 = (3)	Purple (1)	Pink (2)	Make p the same (2)x5 = (4)
Before	352	88	55	275
Change	- 16 u	- 4 u	- 1 u	- 5 u
After	20 p	5 p	4 p	20 p

Number of carnations at first
= 8 b + 5 b
= 13 b

13 b = 143

1 b = 143 ÷ 13 = 11

Number of purple carnations at first
= 8 b
= 8 x 11
= 88

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

88 - 4 u = 5 p --- (1)

55 - 1 u = 4 p --- (2)

Make p the same.

(1)_x4 
352 - 16 u = 20 p --- (3)

(2)_x5 = (4)
275 - 5 u = 20 p --- (4)

(3) = (4)
352 - 16 u = 275 - 5 u
16 u - 5 u = 352 - 275
11 u = 77

1 u = 77 ÷ 11 = 7

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

Answer(s): 21