Mrs Thia had a total of 96 yellow and purple carnations in the ratio of 5 : 3. After she had given away 4 times as many yellow carnations as purple carnations, the number of yellow and purple carnations left was in the ratio of 6 : 5. How many more yellow carnations than purple carnations did she give away?

	Yellow	Purple	Total
Before	5 b	3 b	8 b
Change	- 4 u	- 1 u
After	6 p	5 p

	Make p the same (1)x5 = (3)	Yellow (1)	Purple (2)	Make p the same (2)x6 = (4)
Before	300	60	36	216
Change	- 20 u	- 4 u	- 1 u	- 6 u
After	30 p	6 p	5 p	30 p

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

8 b = 96

1 b = 96 ÷ 8 = 12

Number of yellow carnations at first
= 5 b
= 5 x 12
= 60

Number of purple carnations at first
= 3 b
= 3 x 12
= 36

60 - 4 u = 6 p --- (1)

36 - 1 u = 5 p --- (2)

Make p the same.

(1)_x5 
300 - 20 u = 30 p --- (3)

(2)_x6 = (4)
216 - 6 u = 30 p --- (4)

(3) = (4)
300 - 20 u = 216 - 6 u
20 u - 6 u = 300 - 216
14 u = 84

1 u = 84 ÷ 14 = 6

Number of more yellow carnations than purple carnations that she gave away
= 4 u - 1 u
= 3 u
= 3 x 6
= 18

Answer(s): 18