Mrs Soh had a total of 105 white and pink carnations in the ratio of 5 : 2. After she had given away 4 times as many white carnations as pink carnations, the number of white and pink carnations left was in the ratio of 3 : 2. How many more white carnations than pink carnations did she give away?

	White	Pink	Total
Before	5 b	2 b	7 b
Change	- 4 u	- 1 u
After	3 p	2 p

	Make p the same (1)x2 = (3)	White (1)	Pink (2)	Make p the same (2)x3 = (4)
Before	150	75	30	90
Change	- 8 u	- 4 u	- 1 u	- 3 u
After	6 p	3 p	2 p	6 p

Number of carnations at first
= 5 b + 2 b
= 7 b

7 b = 105

1 b = 105 ÷ 7 = 15

Number of white carnations at first
= 5 b
= 5 x 15
= 75

Number of pink carnations at first
= 2 b
= 2 x 15
= 30

75 - 4 u = 3 p --- (1)

30 - 1 u = 2 p --- (2)

Make p the same.

(1)_x2 
150 - 8 u = 6 p --- (3)

(2)_x3 = (4)
90 - 3 u = 6 p --- (4)

(3) = (4)
150 - 8 u = 90 - 3 u
8 u - 3 u = 150 - 90
5 u = 60

1 u = 60 ÷ 5 = 12

Number of more white carnations than pink carnations that she gave away
= 4 u - 1 u
= 3 u
= 3 x 12
= 36

Answer(s): 36