Mrs Chiam had a total of 90 yellow and purple carnations in the ratio of 7 : 2. After she had given away 6 times as many yellow carnations as purple carnations, the number of yellow and purple carnations left was in the ratio of 8 : 3. How many more yellow carnations than purple carnations did she give away?

	Yellow	Purple	Total
Before	7 b	2 b	9 b
Change	- 6 u	- 1 u
After	8 p	3 p

	Make p the same (1)x3 = (3)	Yellow (1)	Purple (2)	Make p the same (2)x8 = (4)
Before	210	70	20	160
Change	- 18 u	- 6 u	- 1 u	- 8 u
After	24 p	8 p	3 p	24 p

Number of carnations at first
= 7 b + 2 b
= 9 b

9 b = 90

1 b = 90 ÷ 9 = 10

Number of yellow carnations at first
= 7 b
= 7 x 10
= 70

Number of purple carnations at first
= 2 b
= 2 x 10
= 20

70 - 6 u = 8 p --- (1)

20 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
210 - 18 u = 24 p --- (3)

(2)_x8 = (4)
160 - 8 u = 24 p --- (4)

(3) = (4)
210 - 18 u = 160 - 8 u
18 u - 8 u = 210 - 160
10 u = 50

1 u = 50 ÷ 10 = 5

Number of more yellow carnations than purple carnations that she gave away
= 6 u - 1 u
= 5 u
= 5 x 5
= 25

Answer(s): 25