Mrs Lin had a total of 224 purple and yellow carnations in the ratio of 9 : 5. After she had given away 3 times as many purple carnations as yellow carnations, the number of purple and yellow carnations left was in the ratio of 5 : 3. How many more purple carnations than yellow carnations did she give away?

	Purple	Yellow	Total
Before	9 b	5 b	14 b
Change	- 3 u	- 1 u
After	5 p	3 p

	Make p the same (1)x3 = (3)	Purple (1)	Yellow (2)	Make p the same (2)x5 = (4)
Before	432	144	80	400
Change	- 9 u	- 3 u	- 1 u	- 5 u
After	15 p	5 p	3 p	15 p

Number of carnations at first
= 9 b + 5 b
= 14 b

14 b = 224

1 b = 224 ÷ 14 = 16

Number of purple carnations at first
= 9 b
= 9 x 16
= 144

Number of yellow carnations at first
= 5 b
= 5 x 16
= 80

144 - 3 u = 5 p --- (1)

80 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
432 - 9 u = 15 p --- (3)

(2)_x5 = (4)
400 - 5 u = 15 p --- (4)

(3) = (4)
432 - 9 u = 400 - 5 u
9 u - 5 u = 432 - 400
4 u = 32

1 u = 32 ÷ 4 = 8

Number of more purple carnations than yellow carnations that she gave away
= 3 u - 1 u
= 2 u
= 2 x 8
= 16

Answer(s): 16