Mrs Long had a total of 168 white and pink carnations in the ratio of 9 : 5. After she had given away 3 times as many white carnations as pink carnations, the number of white and pink carnations left was in the ratio of 5 : 3. How many more white carnations than pink carnations did she give away?

	White	Pink	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)	White (1)	Pink (2)	Make p the same (2)x5 = (4)
Before	324	108	60	300
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 = 168

1 b = 168 ÷ 14 = 12

Number of white carnations at first
= 9 b
= 9 x 12
= 108

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

108 - 3 u = 5 p --- (1)

60 - 1 u = 3 p --- (2)

Make p the same.

(1)_x3 
324 - 9 u = 15 p --- (3)

(2)_x5 = (4)
300 - 5 u = 15 p --- (4)

(3) = (4)
324 - 9 u = 300 - 5 u
9 u - 5 u = 324 - 300
4 u = 24

1 u = 24 ÷ 4 = 6

Number of more white carnations than pink carnations that she gave away
= 3 u - 1 u
= 2 u
= 2 x 6
= 12

Answer(s): 12