Mrs Chia had a total of 39 yellow and white carnations in the ratio of 9 : 4. After she had given away 3 times as many yellow carnations as white carnations, the number of yellow and white carnations left was in the ratio of 6 : 5. How many more yellow carnations than white carnations did she give away?

	Yellow	White	Total
Before	9 b	4 b	13 b
Change	- 3 u	- 1 u
After	6 p	5 p

	Make p the same (1)x5 = (3)	Yellow (1)	White (2)	Make p the same (2)x6 = (4)
Before	135	27	12	72
Change	- 15 u	- 3 u	- 1 u	- 6 u
After	30 p	6 p	5 p	30 p

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

13 b = 39

1 b = 39 ÷ 13 = 3

Number of yellow carnations at first
= 9 b
= 9 x 3
= 27

Number of white carnations at first
= 4 b
= 4 x 3
= 12

27 - 3 u = 6 p --- (1)

12 - 1 u = 5 p --- (2)

Make p the same.

(1)_x5 
135 - 15 u = 30 p --- (3)

(2)_x6 = (4)
72 - 6 u = 30 p --- (4)

(3) = (4)
135 - 15 u = 72 - 6 u
15 u - 6 u = 135 - 72
9 u = 63

1 u = 63 ÷ 9 = 7

Number of more yellow carnations than white carnations that she gave away
= 3 u - 1 u
= 2 u
= 2 x 7
= 14

Answer(s): 14